http://playpen.farbs.org/index.php?feed=atom&target=76.90.99.69&title=Special%3AContributions PlayPen - User contributions [en-gb] 2026-07-26T11:34:06Z From PlayPen MediaWiki 1.15.1 http://playpen.farbs.org/index.php?title=Matrix_Rep_of_linear_map Matrix Rep of linear map 2019-11-11T01:05:57Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 222222222220222222222222222222222222222222222222<br /> 220022200202022222222022222222220222222222222222<br /> 220222220020222222220220002222222022222222222222<br /> 220220220022220002220220202222222022222222222222<br /> 220220220200222222220220002020222022222222222222<br /> 220220020200220002220222202222222022222222222222<br /> 220022200200222222222022222020220222222222222222<br /> 222222222022222222222222220020022222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 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222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> 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<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Main_LinearAlg1 Main LinearAlg1 2019-11-11T01:01:32Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> fffffffffffffffffffffffffffffffffffffffffffffff1<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> fff9999999999fffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> fff9999999999fffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> fff9999999999fffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> fff9999999999fffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 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ffffffffffffffffffffffffffff99fff999ff9fff9f9fff<br /> ffffffffffffffffffffffffffff9f9ff9f9ff9fff9f9fff<br /> ffffffffffffffffffffffffffff9ff9f999ff9fff9f9999<br /> ................................................<br /> ................................................<br /> ................................................<br /> ...0000000000...................................<br /> ................................................<br /> ...2222222222...................................<br /> ................................................<br /> ...6666666666...................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ..........................................444...<br /> ........................................4444444.<br /> .......................................444444444<br /> .......................................444444444<br /> .......................................444444444<br /> ........................................4444444.<br /> .........................................444444.<br /> ................................................<br /> ....................................1...........<br /> ...........................11111111111111111.111<br /> ...........................11111111111.111111111<br /> ...........................11111111111.111111111<br /> ...........................1111111111111.1111111<br /> ...........................1111111111111.1.11111<br /> ...........................1111.1111111111.11111<br /> ...........................111111111111111.11111<br /> ...........................1111.1111111111.11111<br /> Linear Algebra<br /> L(v j) = <br /> <br /> Each blue line is a link to a page in this project.<br /> Matrices<br /> Matrices<br /> <br /> <br /> Main LinearAlg2<br /> More contents<br /> <br /> <br /> Matrix Rep of linear map<br /> Matrix Rep of linear map<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Matrices Matrices 2019-11-11T00:57:56Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 2222222222222222222222222222202222222cc222cc2222<br /> 23222222222d2222220222220002202202202ccc2cc22222<br /> 23333320202ddd2222000002020200020022220ccc222222<br /> 23232322022d2d2222020202020220220220222cc2222222<br /> 23232320202d2d2222020202000220220220222ccc222222<br /> 22222222222222222202222222022222222222cc2cc22222<br /> 222222222222222222222d222222222222222cc222cc2222<br /> 2222222222ddddddddd2222ddddddddddd22cc22222cc222<br /> 222222222222222222222d22222222222222222222222222<br /> 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000000..........................................<br /> Main LinearAlg1<br /> Linear Algebra home<br /> <br /> <br /> Matrices(1,2)<br /> Matrices(1,2)<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Electronic_Magnet Electronic Magnet 2019-08-03T22:25:30Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> ffffffffffffff0fffffffffffffffffffffffffffffffff<br /> ff000fffffffff0f000fffffffffffffffffffffffffffff<br /> ff0ffff000ff000f0f0fffffffffffffffffffffffffffff<br /> ff000fffffff0f0f000fffffffffffffffffffffffffffff<br /> ff0ffff000ff000f0f0fffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77bbb77777774447aaa77777777777777777777777777777<br /> 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................................................<br /> ................................................<br /> Destination page<br /> Description for player<br /> <br /> <br /> Minkowski Space<br /> Minkowski Space<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=PlayPen:Projects2 PlayPen:Projects2 2019-08-03T22:10:19Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 011111111111111111111111111111111111111111111110<br /> 118888888888888888888888888888888888888888888811<br /> 188880008888888800088888880008888888000888888881<br /> 188803c3088888800100888880ee208888806dd088888881<br /> 18880ccc0800008010108000808ee0800080dd4080008881<br /> 188807770888888001008888803ee0888880baa088888881<br /> 188880008888888800088888880008888888000888888881<br /> 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.......e................................f.......<br /> ................................................<br /> ................................................<br /> ExplosionMan<br /> Explode stuff with Explosion man!<br /> Tictactoe<br /> Play the classic game &quot;Tic-Tac-Toe&quot; with &quot;computer&quot; in PlayPen!\nIt's incredible and super fun!\nRecommended by Stick Figure\n10/25/2011 12:25 (24h format, UTC time)<br /> User:Creativo-golf123<br /> Creativo-golf123 is a creative colaborator! \n As you can see, he added \n some wings and a portal to \n Weird World in the main page, wow!<br /> Weird World<br /> Go to Weird World, is weird but fun! \nRecommended by Creativo-golf123<br /> Welcome To Space!<br /> Portal 2<br /> TimeTon<br /> SkipperThePenguin100's TimeTon adventure project, it's a adventure game which takes on space.<br /> WorldofGoo<br /> Come check out World of Goo, by Darkus2014!<br /> RuinedWorld<br /> Explore a Ruined World<br /> LALALAND<br /> Come to LALALAND, made by Darkus2014's friend!<br /> Diehard<br /> 1%<br /> Linear Algebra<br /> Exploratory medium for linear algebra<br /> UndertaleStartRoom<br /> Let's create Undertale within PlayPen!<br /> Electronic Magnet<br /> Differential forms on Minkowski space?<br /> <br /> <br /> PlayPen:Projects<br /> Previous Page<br /> PlayPen:Projects3<br /> Next Page<br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=PlayPen:Projects2 PlayPen:Projects2 2019-08-03T22:09:51Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 011111111111111111111111111111111111111111111110<br /> 118888888888888888888888888888888888888888888811<br /> 188880008888888800088888880008888888000888888881<br /> 188803c3088888800100888880ee208888806dd088888881<br /> 18880ccc0800008010108000808ee0800080dd4080008881<br /> 188807770888888001008888803ee0888880baa088888881<br /> 188880008888888800088888880008888888000888888881<br /> 188888888888888888888888888888888888888888888881<br /> 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................................................<br /> ................................................<br /> ExplosionMan<br /> Explode stuff with Explosion man!<br /> Tictactoe<br /> Play the classic game &quot;Tic-Tac-Toe&quot; with &quot;computer&quot; in PlayPen!\nIt's incredible and super fun!\nRecommended by Stick Figure\n10/25/2011 12:25 (24h format, UTC time)<br /> User:Creativo-golf123<br /> Creativo-golf123 is a creative colaborator! \n As you can see, he added \n some wings and a portal to \n Weird World in the main page, wow!<br /> Weird World<br /> Go to Weird World, is weird but fun! \nRecommended by Creativo-golf123<br /> Welcome To Space!<br /> Portal 2<br /> TimeTon<br /> SkipperThePenguin100's TimeTon adventure project, it's a adventure game which takes on space.<br /> WorldofGoo<br /> Come check out World of Goo, by Darkus2014!<br /> RuinedWorld<br /> Explore a Ruined World<br /> LALALAND<br /> Come to LALALAND, made by Darkus2014's friend!<br /> Diehard<br /> 1%<br /> Linear Algebra<br /> Exploratory medium for linear algebra<br /> UndertaleStartRoom<br /> Let's create Undertale within PlayPen!<br /> Electronic Magnet<br /> Differential forms on Minkowski space?<br /> <br /> <br /> PlayPen:Projects<br /> Previous Page<br /> PlayPen:Projects3<br /> Next Page<br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Linear_Algebra Linear Algebra 2019-04-08T01:49:41Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> fffff99fffffff99fffff99999ffffffffffffffffffffff<br /> ff9ff9ffff9ffff9f999f9ffffff999fffffffffffffffff<br /> ff9ff9f99f9ffff9ffffff9fffff9f9ffffff99f9f9fffff<br /> ff9ff9ff9f9ffff9f999fff9ffff9f9fffffff9f9f9fffff<br /> ff99f9ff9f9f9ff9ffffff9fffff999f9fff9f9f9f9f9fff<br /> fffff99ff9ffff99fffff9ffff9fff9ffffffff9f9ffffff<br /> ffffffffffff9ffffffff99999ffffff9fff9fffffff9fff<br /> fffffffffff99fffffffffffff9fffff99f99fffffff99ff<br /> ffffffffffffffffffffffffff99ffffffffffffffffffff<br /> 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fffff99f9fff9ff99f9f9fffffffffffffffffffffffffff<br /> f9ff9f9f9ffff9ff9f9f9fffffffffcffffccfcfcfffffff<br /> f9ffff9f9f999f9f9f9f9fffffffffcfcfcfcfcfcfffffff<br /> f99f9ff9fffff9fff9f9ffffffffffccffccfffcffffffff<br /> ffffffffffff9fffffffffffffffffcfcffccfccffffffff<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> .0000000000000000000000000000000000000000000000.<br /> ..a.............................................<br /> .1111.......................111111111...........<br /> ................................................<br /> ...........22......................22...........<br /> ................................................<br /> ..........................33....33..........33..<br /> ................................................<br /> .......444444........................444444444..<br /> ................................................<br /> .......555555...................................<br /> ................................................<br /> .6666...........................................<br /> ................................................<br /> ............................999999999...........<br /> ............................................cc..<br /> ................bbbbb.......................cc..<br /> ................................................<br /> ................................................<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> L(v j) = sum i a ij w i<br /> Used to define matrix rep of a linear map<br /> L and a sub ij<br /> L and a sub ij<br /> the variable j<br /> range, associated variables, row or column, for j<br /> the variable i<br /> range, associated variables, row or column, for i<br /> v j and w i<br /> These are basis vectors, emphasis on the relation between them<br /> v j<br /> <br /> L<br /> The linear map L<br /> key1<br /> key<br /> <br /> <br /> a sub ij<br /> a sub ij<br /> note1<br /> about this horizontal line notation<br /> linear combination in terms of basis is unique<br /> linear combination in terms of basis is unique<br /> Main LinearAlg1<br /> Main LinearAlg1<br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=New_L_and_a_ij New L and a ij 2019-04-08T01:39:49Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 11777711711b77777777777771777777777777177777777b<br /> 177b77717171777777777777177711177777777177777777<br /> 177177717111777711117777177117177777777177777777<br /> 177177717171777777777777177177171777177177777777<br /> 177117717117777777777777177111177777777177777777<br /> 177777717777777711111777717777171777171777777777<br /> 117777117111177777777777777777771171177777777777<br /> 777777777171b77777777777777777777773777777777777<br /> 77777777711177777777777777777bbbbbb7bbbbbbbbbbbb<br /> 77777777777177777bbbbbbbbbbbbb777773777777777777<br /> 77777777777777777b777777777777777733777777777777<br /> 7777777777777777bb777711777777777377b77777771777<br /> bbbbbbbbbbbbb777b7777717777777777377777777771117<br /> 7777777777bbb777b7777117777777777377777777777717<br /> bbbbbbbbbbbbb777b7777117777777777377777777777711<br /> 7777777777777777b7777177777777777377777777777771<br /> 7777777777777777b7777177777777777377777777777771<br /> 7777777777777777bb777177777777777377777777777771<br /> 77777777777777777b777177777777777377777777777771<br /> 77777777777777777b777177777777777377777777777771<br /> 77777777777777777b777177777777777777777777777771<br /> 77777777777777777b377177777777733b77777777777771<br /> 77777777777777777b777177777777337377777777777771<br /> 77777777777777777b377133333337377377777773333371<br /> 77777777777777777b377177777777333373777377777771<br /> 77777777777777777b337177777777777377777777777771<br /> 77777777777777777b7b7177777777777773777377777771<br /> 77777777777777777b777177777777777373373377777771<br /> 72777222727772777b777177777777777377777777777771<br /> 72227222727272777b777117777777777377777777777711<br /> 72727277722222777b777711177777777377777777777717<br /> 72727222772727777b777771177777777377777777777117<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> alpha and beta<br /> what are these?<br /> <br /> <br /> new L and a ij<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=L_and_a_sub_ij L and a sub ij 2019-04-08T01:34:51Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 117777117117775777777777717777777777771777777777<br /> 177777717171775777777777177711177777777177777777<br /> 177177717111775711117777177117177777777177777777<br /> 177177717171775777777777177177171777177177777777<br /> 177117717117775777777777177111177777777177777777<br /> 177777717777775711111777717777171777171777777777<br /> 117777117111175777777777777777771171177777777777<br /> 777777777171775777777777777777777773777777777777<br /> 777777777111775777777777777777777777777777777777<br /> 777777777771775777777777777777777773777777777777<br /> 777777777777775777777777777777777733777777777777<br /> 5bbbbbbbbbbbb54555555711777777777377777777771777<br /> 777777777777775777777717777777777377777777771117<br /> 777777777777775777777117777777777377777777777717<br /> 777777777777775777777117777777777377777777777711<br /> 777777777777775777777177777777777377777777777771<br /> 777777777777775777777177777777777377777777777771<br /> 777777777777775777777177777777777377777777777771<br /> 777777777777775777777177777777777377777777777771<br /> 777777777777775777777177777777777377777777777771<br /> 777777777777775777777177777777777777777777777771<br /> 777777777777775777377177777777733377777777777771<br /> 777777777777775777777177777777337377777777777771<br /> 777777777777775777377133333337377377777773333371<br /> 777777777777775777377177777777333373777377777771<br /> 777777777777775777337177777777777377777777777771<br /> 777777777777775777777177777777777773777377777771<br /> 777777777777775777777177777777777373373377777771<br /> 727772227277725777777177777777777377777777777771<br /> 722272227272725777777117777777777377777777777711<br /> 727272777222225777777711177777777377777777777717<br /> 727272227727275777777771177777777377777777777117<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ...........2....................................<br /> .22222222.22.2..................................<br /> .2222222222222..................................<br /> .2222222222222..................................<br /> ..222222222222..................................<br /> alpha and beta<br /> what are these?<br /> <br /> <br /> new L and a ij<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Matrices Matrices 2019-04-08T01:28:32Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 2222222222222222222222222222202222222cc222cc2222<br /> 23222222222d2222220222220002202202202ccc2cc22222<br /> 23333320202ddd2222000002020200020022220ccc222222<br /> 23232322022d2d2222020202020220220220222cc2222222<br /> 23232320202d2d2222020202000220220220222ccc222222<br /> 22222222222222222202222222022222222222cc2cc22222<br /> 222222222222222222222d222222222222222cc222cc2222<br /> 2222222222ddddddddd2222ddddddddddd22cc22222cc222<br /> 222222222222222222222d22222222222222222222222222<br /> 22222222222222222222dd22222222222222222222222222<br /> 222222322002222222222222222222222000222222222222<br /> 222222322022222222222222222222222220222222222222<br /> 222222322020002222222222200022222220222222222222<br /> 222222322020202222202020202022222220222222222222<br /> 222222322020002020222222200020200220222222222222<br /> 222222322022202020222222222020200020222222222222<br /> 222222222022222020222222222220202020222222222222<br /> 222222322022222222222222220222222220222222f22222<br /> 2222222220222202222222222222222222202222222f2222<br /> 22222232202222222222222222022222222022fffff2f222<br /> 2222223320222202222222222222222222202222222f2222<br /> 222222222022222222222222222222222220222222f22222<br /> 222222322022220222222222220222222220222222222222<br /> 222222322022222222222222222222222220222222222222<br /> 222222322020002222222222222222222220222222222222<br /> 2222223220202022222c2c2c222222222220222222222222<br /> 222222322020002222222222200022222220222222222222<br /> 222222322022202cccc2c222202022222220222222222222<br /> 21221232200222c0c2c2c222200066226200222222222222<br /> 22112222222222c2c2c2c222222062626666622222222222<br /> 221122222222222222222222222262626262622222222222<br /> 212212222222222222222222222222222222222222222222<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> 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................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> 00000...........................................<br /> 000000..........................................<br /> 000000..........................................<br /> 000000..........................................<br /> 000000..........................................<br /> Main LinearAlg1<br /> Linear Algebra home<br /> <br /> <br /> Matrices(1,2)<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Matrices(1,2) Matrices(1,2) 2019-04-08T01:26:23Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> f22222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222000002222222222222<br /> 222222222222222222222000222222222222202220000222<br /> 222222222222022202222222220202022222220220222222<br /> 222222222222c020c2202022222022000002002020000222<br /> 222222222222020202222000220202020202220220222222<br /> 222222222222c222c2202020222222222222202220222222<br /> 222222222222022202222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 22222222222c222222222222222222222222222222222222<br /> 222222222c2c202222222222222222222222222222222222<br /> 222222222ccccc2222222222222222222222222222222222<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> 0...............................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> .....................2.2........................<br /> .....................2.2........................<br /> .....................2.2........................<br /> .....................2222.......................<br /> ......................2.2.......................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> Matrices<br /> To the left<br /> <br /> <br /> The set n<br /> The set n<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Matrices Matrices 2019-04-08T01:15:46Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 2222222222222222222222222222202222222cc222cc2222<br /> 23222222222d2222220222220002202202202ccc2cc22222<br /> 23333320202ddd2222000002020200020022220ccc222222<br /> 23232322022d2d2222020202020220220220222cc2222222<br /> 23232320202d2d2222020202000220220220222ccc222222<br /> 22222222222222222202222222022222222222cc2cc22222<br /> 222222222222222222222d222222222222222cc222cc2222<br /> 2222222222ddddddddd2222ddddddddddd22cc22222cc222<br /> 222222222222222222222d22222222222222222222222222<br /> 22222222222222222222dd22222222222222222222222222<br /> 222222322002222222222222222222222000222222222222<br /> 222222322022222222222222222222222220222222222222<br /> 222222322020002222222222200022222220222222222222<br /> 222222322020202222202020202022222220222222222222<br /> 222222322020002020222222200020200220222222222222<br /> 222222322022202020222222222020200020222222222222<br /> 222222222022222020222222222220202020222222222222<br /> 222222322022222222222222220222222220222222f22222<br /> 2222222220222202222222222222222222202222222f2222<br /> 22222232202222222222222222022222222022fffff2f222<br /> 2222223320222202222222222222222222202222222f2222<br /> 222222222022222222222222222222222220222222f22222<br /> 222222322022220222222222220222222220222222222222<br /> 222222322022222222222222222222222220222222222222<br /> 222222322020000222222222222222222220222222222222<br /> 2222223220202022222c2c2c222222222220222222222222<br /> 222222322020002222222222200022222220222222222222<br /> 22222232202220ccccc2c222202022222220222222222222<br /> 21221232200222c2c2c2c222200066226200222222222222<br /> 22112222222222c2c2c2c222222062626666622222222222<br /> 221122222222222222222222222262626262622222222222<br /> 212212222222222222222222222222222222222222222222<br /> ................................................<br /> ................................................<br /> ................................................<br /> 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......................................2222222...<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> 00000...........................................<br /> 000000..........................................<br /> 000000..........................................<br /> 000000..........................................<br /> 000000..........................................<br /> Main LinearAlg1<br /> Linear Algebra home<br /> <br /> <br /> Matrices(1,2)<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Matrices Matrices 2019-04-07T23:37:49Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 2222222222222222222222222222202222222cc222cc2222<br /> 2022222220222222220222220000202202202ccc2cc22222<br /> 200020202000002222000002020200020022220ccc222222<br /> 202022022020202222020202020220220220222cc2222222<br /> 202020202020202222020202000220220220222ccc222222<br /> 22222222222222222202222222022222222222cc2cc22222<br /> 2222222222222222222222222222222222222cc222cc2222<br /> 222222222222222222222222222222222222cc22222cc222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 212212222222222222222222222222222222222222222222<br /> 221122222222222222222222222222222222222222222222<br /> 221122222222222222222222222222222222222222222222<br /> 212212222222222222222222222222222222222222222222<br /> ................................................<br /> ................................................<br /> ................................................<br /> 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<p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 2222222222222222222222222222202222222cc222cc2222<br /> 2022222220222222220222220000202202202ccc2cc22222<br /> 200020202000002222000002020200020022220ccc222222<br /> 202022022020202222020202020220220220222cc2222222<br /> 202020202020202222020202000220220220222ccc222222<br /> 22222222222222222202222222022222222222cc2cc22222<br /> 2222222222222222222222222222222222222cc222cc2222<br /> 222222222222222222222222222222222222cc22222cc222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 222222222222222222222222222222222222222222222222<br /> 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................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> Destination page<br /> Description for player<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Main_LinearAlg1 Main LinearAlg1 2019-04-07T23:31:20Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> fffffffffffffffffffffffffffffffffffffffffffffff1<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> fff9999999999fffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> fff9999999999fffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> fff9999999999fffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> fff9999999999fffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> fff9999999999fffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffff1fff<br /> fffffffffffffffffffffffffffffffffffffffffffff1ff<br /> ffffffffffffffffffffffffffffffffffffffff11111f1f<br /> fffffffffffffffffffffffffffffffffffffffffffff1ff<br /> ffffffffffffffffffffffffffffffffffffffffffff1fff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffff9999fff9ff99f99f9999<br /> ffffffffffffffffffffffffffff9ff9fff9ff9f9f9f9ff9<br /> ffffffffffffffffffffffffffff9ff9fff9ff9f9f9f9ff9<br /> ffffffffffffffffffffffffffff9999fff9ff9f9f9f9999<br /> ffffffffffffffffffffffffffff99fff999ff9fff9f9fff<br /> ffffffffffffffffffffffffffff9f9ff9f9ff9fff9f9fff<br /> ffffffffffffffffffffffffffff9ff9f999ff9fff9f9999<br /> ................................................<br /> ................................................<br /> ................................................<br /> ...0000000000...................................<br /> ................................................<br /> ...2222222222...................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ..........................................444...<br /> ........................................4444444.<br /> .......................................444444444<br /> .......................................444444444<br /> .......................................444444444<br /> ........................................4444444.<br /> .........................................444444.<br /> ................................................<br /> ....................................1...........<br /> ...........................11111111111111111.111<br /> ...........................11111111111.111111111<br /> ...........................11111111111.111111111<br /> ...........................1111111111111.1111111<br /> ...........................1111111111111.1.11111<br /> ...........................1111.1111111111.11111<br /> ...........................111111111111111.11111<br /> ...........................1111.1111111111.11111<br /> Linear Algebra<br /> L(v j) = <br /> <br /> Each blue line is a link to a page in this project.<br /> Matrices<br /> Matrices<br /> <br /> <br /> Main LinearAlg2<br /> More contents<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=V_j_and_w_i V j and w i 2019-04-06T15:49:39Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 888188888818888888888888888888888888e88888888888<br /> 88188888888188888888888888888888888e888888888888<br /> 8818118888881888888888888888888888e8eeee88888888<br /> 11888181888818888888888888888888888e888888888888<br /> 881881818888818888888888888888888888e88888888888<br /> 881888188188188888888888888888888888888888888888<br /> 818888888888188888888888888888888888888888888888<br /> 881888888188818888888888888888888888888888888888<br /> 888188881188188188888188888881888888888888888888<br /> 888888888881188881188188888881111188888888888888<br /> 888888888888888188888188888881818188888888888888<br /> 888888888888881181188181818181818188888888888888<br /> 888818888888888888888888888888888888888888888888<br /> 888188888888881888888888888888888888888888888888<br /> 881888888888888188888888888888888888888888888888<br /> 888181188818888818888888888888888888888888888888<br /> 888188181818888188888888888888888888888888888888<br /> 811888181818188188888888888888888888888888888888<br /> 888188818188888811888888888888888888888888888888<br /> 888188888888188188888888818888888188888888888888<br /> 881888888888118188188118818888888111888888888888<br /> 888188888888888818888888818888888181888888888888<br /> 888818888888888188188118818888888181888888888888<br /> 888888888888881888118888818181818181888888888888<br /> 000000008888888888888888888888888888888888888888<br /> 888888800000000000000000000000000000000000000000<br /> 118888888888888888888888888888888888888888888888<br /> 818188881181888188811888888888811881818188888888<br /> 818181818881181188881818181888188881818188888888<br /> 881888811188181888881818188888111881818188888888<br /> 888881818888111888888181881888188888181888888888<br /> 888811881188818888888888881188811888888888888888<br /> ..................................00.0000.......<br /> ..................................0000000.......<br /> .................................00000000.......<br /> ..................................0000000.......<br /> ..................................0000000.......<br /> .....................................0..........<br /> .....................................0..........<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> Linear Algebra<br /> Go back<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=L(v_j)_%3D_sum_i_a_ij_w_i L(v j) = sum i a ij w i 2019-04-06T15:22:13Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> d11dddddddddd11ddddddddddddddddddddddddddddddddd<br /> d1dddddd1dddddd1dddddddddddddddddddddddddddddddd<br /> d1dddddd1dddddd1ddddddddd1dddddddddddddddddddddd<br /> d1d11ddd1dddddd1ddddddddd1dddddddddddddddddddddd<br /> d1dd11d11dddddd1ddddddddd1dddddddd11d1d111dddddd<br /> d1ddd1d1ddddddd1ddddddddd111d111dd1dddd1dddddddd<br /> d11dd111dd1dddd111dd1d11d1d1d111dd11d1d111dddddd<br /> d11ddd11dddddddd11ddddddd111d111d111d1d111dddddd<br /> 111dddd1dd1ddddd1dddddddddddddd1dddddddddddddddd<br /> dd1ddddddd1ddddd11dddddddddddddddddddddddddddd1d<br /> dd1ddddddd1dddddd1dddddd11dddddddddddddd1dddd11d<br /> d11dddddd11dddddd1dddddd1ddddddddd111ddd1ddd11dd<br /> d1ddddddddddddddd1ddddd1111ddddddd1ddddd11dd1ddd<br /> d1ddddddddddddddd1dddddd1dddd1111d1dddddd1dd1ddd<br /> d1111ddddddddddd11dddddd1dddd1dd1d1dddddd1111ddd<br /> ddddddddddddddd11ddddddd1dddd1d11d1ddddddd11dddd<br /> ddddddddddddddddddddddddddddd111ddddddddddd1dddd<br /> d1ddddd1dddddddddddddddddddddddddddddd1ddddddddd<br /> d1dddd11dddddd1dddddddddddddddddddddd11ddddddddd<br /> d1dddd1dd1ddd11ddd11ddddddd1ddddddddd1dddddddddd<br /> d1dddd1ddd1dd1ddddd1ddd111d11ddddddd11dddddddddd<br /> d11ddd11dd1111ddddd11d11dddd1dd11ddd1ddddddddddd<br /> dd111dd1ddd11ddd1ddd1d111dddd1d11ddd1ddddddddddd<br /> ddddddd11ddd1ddddddd1d1d111dd1d111d11ddddddddddd<br /> dddddddd11dddddd1ddd1d11ddddd111d111dddddddddddd<br /> ddddddddddddddd11ddd1dd11d1ddd1ddd11dddddddddddd<br /> ddddddddddddddddddd1dddd111ddddddd11dddddddddddd<br /> dd1dddddddddddddddd1dddddddddddddddddddddddddddd<br /> d1dddddddddddddddddddddddddddddddddddddddddddddd<br /> 1d111111111ddddddddddddddddddddddddddddddddddddd<br /> d1dddddddddddddddddddddddddddddddddddddddddddddd<br /> dd1ddddddddddddddddddddddddddddddddddddddddddddd<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> 0000.000000.....................................<br /> 00000000000.....................................<br /> 00000000000.....................................<br /> 00000000000.....................................<br /> 00000000000.....................................<br /> Linear Algebra<br /> Go back<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Key1 Key1 2019-04-06T15:16:43Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 8848ccccccccccccccccc888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 8878ccccccccccccccccc888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 88b8ccccccccccccccccc888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> ................................................<br /> ................................................<br /> ................................................<br /> ..0.00000000000000000...........................<br /> ................................................<br /> ..2.22222222222222222...........................<br /> ................................................<br /> ..4.44444.44444444444...........................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> <br /> Random Remarks<br /> <br /> <br /> <br /> to indicate a line<br /> <br /> <br /> <br /> indicates the part of the equation we are looking at<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Main_LinearAlg1 Main LinearAlg1 2019-04-06T15:15:57Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> fff9999999999fffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> fff9999999999fffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> fff9999999999fffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> fff9999999999fffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> fff9999999999fffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffff9999fff9ff99f99f9999<br /> ffffffffffffffffffffffffffff9ff9fff9ff9f9f9f9ff9<br /> ffffffffffffffffffffffffffff9ff9fff9ff9f9f9f9ff9<br /> ffffffffffffffffffffffffffff9999fff9ff9f9f9f9999<br /> ffffffffffffffffffffffffffff99fff999ff9fff9f9fff<br /> ffffffffffffffffffffffffffff9f9ff9f9ff9fff9f9fff<br /> ffffffffffffffffffffffffffff9ff9f999ff9fff9f9999<br /> ................................................<br /> ................................................<br /> ................................................<br /> ...0000000000...................................<br /> ................................................<br /> ...2222222222...................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> Linear Algebra<br /> L(v j) = <br /> <br /> Each blue line is a link to a page in this project.<br /> Matrices<br /> Matrices<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Linear_Algebra Linear Algebra 2019-04-06T06:24:25Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> fffff99fffffff99fffff99999ffffffffffffffffffffff<br /> ff9ff9ffff9ffff9f999f9ffffff999fffffffffffffffff<br /> ff9ff9f99f9ffff9ffffff9fffff9f9ffffff99f9f9fffff<br /> ff9ff9ff9f9ffff9f999fff9ffff9f9fffffff9f9f9fffff<br /> ff99f9ff9f9f9ff9ffffff9fffff999f9fff9f9f9f9f9fff<br /> fffff99ff9ffff99fffff9ffff9fff9ffffffff9f9ffffff<br /> ffffffffffff9ffffffff99999ffffff9fff9fffffff9fff<br /> fffffffffff99fffffffffffff9fffff99f99fffffff99ff<br /> ffffffffffffffffffffffffff99ffffffffffffffffffff<br /> 7bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb7<br /> ff4fffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb77777777777777777777777bbbbbbbbb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777bb7777777777777777777777bb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777777777777777777bb7777bb7777777777bb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb777777777777777777777777bbbbbbbbb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb77777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb7777777777777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffddff<br /> ffffffffffffffffffffffffffffffffffffffffffffddff<br /> 000000000000000000000000000000000000000000000000<br /> fffff99f9fff9ff99f9f9fffffffffffffffffffffffffff<br /> f9ff9f9f9ffff9ff9f9f9fffffffffcffffccfcfcfffffff<br /> f9ffff9f9f999f9f9f9f9fffffffffcfcfcfcfcfcfffffff<br /> f99f9ff9fffff9fff9f9ffffffffffccffccfffcffffffff<br /> ffffffffffff9fffffffffffffffffcfcffccfccffffffff<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> .0000000000000000000000000000000000000000000000.<br /> ..a.............................................<br /> .1111.......................111111111...........<br /> ................................................<br /> ...........22......................22...........<br /> ................................................<br /> ..........................33....33..........33..<br /> ................................................<br /> .......444444........................444444444..<br /> ................................................<br /> .......555555...................................<br /> ................................................<br /> .6666...........................................<br /> ................................................<br /> ................................................<br /> ............................................cc..<br /> ............................................cc..<br /> ................................................<br /> ................................................<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> L(v j) = sum i a ij w i<br /> Used to define matrix rep of a linear map<br /> L and a sub ij<br /> L and a sub ij<br /> the variable j<br /> range, associated variables, row or column, for j<br /> the variable i<br /> range, associated variables, row or column, for i<br /> v j and w i<br /> These are basis vectors, emphasis on the relation between them<br /> v j<br /> <br /> L<br /> The linear map L<br /> key1<br /> key<br /> <br /> <br /> <br /> <br /> note1<br /> about this horizontal line notation<br /> <br /> <br /> Main LinearAlg1<br /> Main LinearAlg1<br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Key1 Key1 2019-04-06T02:30:46Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 8848ccccccccccccccccc888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 8878ccccccccccccccccc888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 88b8ccccccccccccccccc888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> ................................................<br /> ................................................<br /> ................................................<br /> ..0.00000000000000000...........................<br /> ................................................<br /> ..2.22222222222222222...........................<br /> ................................................<br /> ..4.44444.44444444444...........................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> page0000111111<br /> Random Remarks<br /> <br /> <br /> page 00000011101<br /> to indicate a line<br /> <br /> <br /> page 00101110001<br /> indicates the part of the equation we are looking at<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Key1 Key1 2019-04-06T01:55:16Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 8848ccccccccccccccccc888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 8878ccccccccccccccccc888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 88b8ccccccccccccccccc888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> 888888888888888888888888888888888888888888888888<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> 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................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> page0000111111<br /> Random Remarks<br /> <br /> <br /> page 00000011101<br /> to indicate a line<br /> <br /> <br /> page 00101110001<br /> indicates the part of the equation we are looking at<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Linear_Algebra Linear Algebra 2019-04-06T01:51:55Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> fffff99fffffff99fffff99999ffffffffffffffffffffff<br /> ff9ff9ffff9ffff9f999f9ffffff999fffffffffffffffff<br /> ff9ff9f99f9ffff9ffffff9fffff9f9ffffff99f9f9fffff<br /> ff9ff9ff9f9ffff9f999fff9ffff9f9fffffff9f9f9fffff<br /> ff99f9ff9f9f9ff9ffffff9fffff999f9fff9f9f9f9f9fff<br /> fffff99ff9ffff99fffff9ffff9fff9ffffffff9f9ffffff<br /> ffffffffffff9ffffffff99999ffffff9fff9fffffff9fff<br /> fffffffffff99fffffffffffff9fffff99f99fffffff99ff<br /> ffffffffffffffffffffffffff99ffffffffffffffffffff<br /> 7bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb7<br /> ff4fffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb77777777777777777777777bbbbbbbbb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777bb7777777777777777777777bb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777777777777777777bb7777bb7777777777bb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb777777777777777777777777bbbbbbbbb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb77777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb7777777777777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 000000000000000000000000000000000000000000000000<br /> fffff99f9fff9ff99f9f9fffffffffffffffffffffffffff<br /> f9ff9f9f9ffff9ff9f9f9fffffffffcffffccfcfcfffffff<br /> f9ffff9f9f999f9f9f9f9fffffffffcfcfcfcfcfcfffffff<br /> f99f9ff9fffff9fff9f9ffffffffffccffccfffcffffffff<br /> ffffffffffff9fffffffffffffffffcfcffccfccffffffff<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> .0000000000000000000000000000000000000000000000.<br /> ..a.............................................<br /> .1111.......................111111111...........<br /> ................................................<br /> ...........22......................22...........<br /> ................................................<br /> ..........................33....33..........33..<br /> ................................................<br /> .......444444........................444444444..<br /> ................................................<br /> .......555555...................................<br /> ................................................<br /> .6666...........................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> L(v j) = sum i a ij w i<br /> Used to define matrix rep of a linear map<br /> L and a sub ij<br /> L and a sub ij<br /> the variable j<br /> range, associated variables, row or column, for j<br /> the variable i<br /> range, associated variables, row or column, for i<br /> v j and w i<br /> These are basis vectors, emphasis on the relation between them<br /> v j<br /> <br /> L<br /> The linear map L<br /> key1<br /> key<br /> <br /> <br /> <br /> <br /> note1<br /> about this horizontal line notation<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Linear_Algebra Linear Algebra 2019-04-06T01:46:52Z <p>76.90.99.69:&#32;I think if a new page has the same name as an old one then you go to the old page</p> <hr /> <div>&lt;ppimage&gt;<br /> fffff99fffffff99fffff99999ffffffffffffffffffffff<br /> ff9ff9ffff9ffff9f999f9ffffff999fffffffffffffffff<br /> ff9ff9f99f9ffff9ffffff9fffff9f9ffffff99f9f9fffff<br /> ff9ff9ff9f9ffff9f999fff9ffff9f9fffffff9f9f9fffff<br /> ff99f9ff9f9f9ff9ffffff9fffff999f9fff9f9f9f9f9fff<br /> fffff99ff9ffff99fffff9ffff9fff9ffffffff9f9ffffff<br /> ffffffffffff9ffffffff99999ffffff9fff9fffffff9fff<br /> fffffffffff99fffffffffffff9fffff99f99fffffff99ff<br /> ffffffffffffffffffffffffff99ffffffffffffffffffff<br /> 7bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb7<br /> ff4fffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb77777777777777777777777bbbbbbbbb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777bb7777777777777777777777bb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777777777777777777bb7777bb7777777777bb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb777777777777777777777777bbbbbbbbb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb77777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb7777777777777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 000000000000000000000000000000000000000000000000<br /> fffff99f9fff9ff99f9f9fffffffffffffffffffffffffff<br /> f9ff9f9f9ffff9ff9f9f9fffffffffcffffccfcfcfffffff<br /> f9ffff9f9f999f9f9f9f9fffffffffcfcfcfcfcfcfffffff<br /> f99f9ff9fffff9fff9f9ffffffffffccffccfffcffffffff<br /> ffffffffffff9fffffffffffffffffcfcffccfccffffffff<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> .0000000000000000000000000000000000000000000000.<br /> ..a.............................................<br /> .1111.......................111111111...........<br /> ................................................<br /> ...........22......................22...........<br /> ................................................<br /> ..........................33....33..........33..<br /> ................................................<br /> .......444444........................444444444..<br /> ................................................<br /> .......555555...................................<br /> ................................................<br /> .6666...........................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> L(v j) = sum i a ij w i<br /> Used to define matrix rep of a linear map<br /> L and a sub ij<br /> L and a sub ij<br /> the variable j<br /> range, associated variables, row or column, for j<br /> the variable i<br /> range, associated variables, row or column, for i<br /> v j and w i<br /> These are basis vectors, emphasis on the relation between them<br /> v j<br /> <br /> L<br /> The linear map L<br /> key<br /> key<br /> <br /> <br /> <br /> <br /> note1<br /> about this horizontal line notation<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Linear_Algebra Linear Algebra 2019-04-06T01:44:24Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> fffff99fffffff99fffff99999ffffffffffffffffffffff<br /> ff9ff9ffff9ffff9f999f9ffffff999fffffffffffffffff<br /> ff9ff9f99f9ffff9ffffff9fffff9f9ffffff99f9f9fffff<br /> ff9ff9ff9f9ffff9f999fff9ffff9f9fffffff9f9f9fffff<br /> ff99f9ff9f9f9ff9ffffff9fffff999f9fff9f9f9f9f9fff<br /> fffff99ff9ffff99fffff9ffff9fff9ffffffff9f9ffffff<br /> ffffffffffff9ffffffff99999ffffff9fff9fffffff9fff<br /> fffffffffff99fffffffffffff9fffff99f99fffffff99ff<br /> ffffffffffffffffffffffffff99ffffffffffffffffffff<br /> 7bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb7<br /> ff4fffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb77777777777777777777777bbbbbbbbb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777bb7777777777777777777777bb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777777777777777777bb7777bb7777777777bb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb777777777777777777777777bbbbbbbbb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb77777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb7777777777777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 000000000000000000000000000000000000000000000000<br /> fffff99f9fff9ff99f9f9fffffffffffffffffffffffffff<br /> f9ff9f9f9ffff9ff9f9f9fffffffffcffffccfcfcfffffff<br /> f9ffff9f9f999f9f9f9f9fffffffffcfcfcfcfcfcfffffff<br /> f99f9ff9fffff9fff9f9ffffffffffccffccfffcffffffff<br /> ffffffffffff9fffffffffffffffffcfcffccfccffffffff<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> .0000000000000000000000000000000000000000000000.<br /> ..a.............................................<br /> .1111.......................111111111...........<br /> ................................................<br /> ...........22......................22...........<br /> ................................................<br /> ..........................33....33..........33..<br /> ................................................<br /> .......444444........................444444444..<br /> ................................................<br /> .......555555...................................<br /> ................................................<br /> .6666...........................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> L(v j) = sum i a ij w i<br /> Used to define matrix rep of a linear map<br /> L and a sub ij<br /> L and a sub ij<br /> j<br /> range, associated variables, row or column, for j<br /> i<br /> range, associated variables, row or column, for i<br /> v j and w i<br /> These are basis vectors, emphasis on the relation between them<br /> v j<br /> <br /> L<br /> The linear map L<br /> key<br /> key<br /> <br /> <br /> <br /> <br /> note1<br /> about this horizontal line notation<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Linear_Algebra Linear Algebra 2019-04-06T01:43:07Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> fffff99fffffff99fffff99999ffffffffffffffffffffff<br /> ff9ff9ffff9ffff9f999f9ffffff999fffffffffffffffff<br /> ff9ff9f99f9ffff9ffffff9fffff9f9ffffff99f9f9fffff<br /> ff9ff9ff9f9ffff9f999fff9ffff9f9fffffff9f9f9fffff<br /> ff99f9ff9f9f9ff9ffffff9fffff999f9fff9f9f9f9f9fff<br /> fffff99ff9ffff99fffff9ffff9fff9ffffffff9f9ffffff<br /> ffffffffffff9ffffffff99999ffffff9fff9fffffff9fff<br /> fffffffffff99fffffffffffff9fffff99f99fffffff99ff<br /> ffffffffffffffffffffffffff99ffffffffffffffffffff<br /> 7bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb7<br /> ff4fffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb77777777777777777777777bbbbbbbbb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777bb7777777777777777777777bb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777777777777777777bb7777bb7777777777bb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb777777777777777777777777bbbbbbbbb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb77777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb7777777777777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 000000000000000000000000000000000000000000000000<br /> fffff99f9fff9ff99f9f9fffffffffffffffffffffffffff<br /> f9ff9f9f9ffff9ff9f9f9fffffffffcffffccfcfcfffffff<br /> f9ffff9f9f999f9f9f9f9fffffffffcfcfcfcfcfcfffffff<br /> f99f9ff9fffff9fff9f9ffffffffffccffccfffcffffffff<br /> ffffffffffff9fffffffffffffffffcfcffccfccffffffff<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> .0000000000000000000000000000000000000000000000.<br /> ..a.............................................<br /> .1111.......................111111111...........<br /> ................................................<br /> ...........22......................22...........<br /> ................................................<br /> ..........................33....33..........33..<br /> ................................................<br /> .......444444........................444444444..<br /> ................................................<br /> .......555555...................................<br /> ................................................<br /> .6666...........................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> L(v j) = sum i a ij w i<br /> Used to define matrix rep of a linear map<br /> L and a sub ij<br /> L and a sub ij<br /> j<br /> range, associated variables, row or column, for j<br /> i<br /> range, associated variables, row or column, for i<br /> v_j and w_i<br /> These are basis vectors, emphasis on the relation between them<br /> v_j<br /> <br /> L<br /> The linear map L<br /> key<br /> key<br /> <br /> <br /> <br /> <br /> note1<br /> about this horizontal line notation<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Linear_Algebra Linear Algebra 2019-04-06T01:41:03Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> fffff99fffffff99fffff99999ffffffffffffffffffffff<br /> ff9ff9ffff9ffff9f999f9ffffff999fffffffffffffffff<br /> ff9ff9f99f9ffff9ffffff9fffff9f9ffffff99f9f9fffff<br /> ff9ff9ff9f9ffff9f999fff9ffff9f9fffffff9f9f9fffff<br /> ff99f9ff9f9f9ff9ffffff9fffff999f9fff9f9f9f9f9fff<br /> fffff99ff9ffff99fffff9ffff9fff9ffffffff9f9ffffff<br /> ffffffffffff9ffffffff99999ffffff9fff9fffffff9fff<br /> fffffffffff99fffffffffffff9fffff99f99fffffff99ff<br /> ffffffffffffffffffffffffff99ffffffffffffffffffff<br /> 7bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb7<br /> ff4fffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb77777777777777777777777bbbbbbbbb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777bb7777777777777777777777bb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777777777777777777bb7777bb7777777777bb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb777777777777777777777777bbbbbbbbb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb77777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb7777777777777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 000000000000000000000000000000000000000000000000<br /> fffff99f9fff9ff99f9f9fffffffffffffffffffffffffff<br /> f9ff9f9f9ffff9ff9f9f9fffffffffcffffccfcfcfffffff<br /> f9ffff9f9f999f9f9f9f9fffffffffcfcfcfcfcfcfffffff<br /> f99f9ff9fffff9fff9f9ffffffffffccffccfffcffffffff<br /> ffffffffffff9fffffffffffffffffcfcffccfccffffffff<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> .0000000000000000000000000000000000000000000000.<br /> ..a.............................................<br /> .1111.......................111111111...........<br /> ................................................<br /> ...........22......................22...........<br /> ................................................<br /> ..........................33....33..........33..<br /> ................................................<br /> .......444444........................444444444..<br /> ................................................<br /> .......555555...................................<br /> ................................................<br /> .6666...........................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> L(v j) = sum i a ij w i<br /> Used to define matrix rep of a linear map<br /> L and a sub ij<br /> L and a sub ij<br /> j<br /> range, associated variables, row or column, for j<br /> i<br /> range, associated variables, row or column, for i<br /> v_j and w_i<br /> These are basis vectors, emphasis on the relation between them<br /> v_j<br /> <br /> L<br /> The linear map L<br /> key<br /> key<br /> <br /> <br /> <br /> <br /> note<br /> about this horizontal line notation<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Linear_Algebra Linear Algebra 2019-04-06T01:27:54Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> fffff99fffffff99fffff99999ffffffffffffffffffffff<br /> ff9ff9ffff9ffff9f999f9ffffff999fffffffffffffffff<br /> ff9ff9f99f9ffff9ffffff9fffff9f9ffffff99f9f9fffff<br /> ff9ff9ff9f9ffff9f999fff9ffff9f9fffffff9f9f9fffff<br /> ff99f9ff9f9f9ff9ffffff9fffff999f9fff9f9f9f9f9fff<br /> fffff99ff9ffff99fffff9ffff9fff9ffffffff9f9ffffff<br /> ffffffffffff9ffffffff99999ffffff9fff9fffffff9fff<br /> fffffffffff99fffffffffffff9fffff99f99fffffff99ff<br /> ffffffffffffffffffffffffff99ffffffffffffffffffff<br /> 7bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb7<br /> ff4fffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb77777777777777777777777bbbbbbbbb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777bb7777777777777777777777bb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777777777777777777bb7777bb7777777777bb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb777777777777777777777777bbbbbbbbb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb77777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb7777777777777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 000000000000000000000000000000000000000000000000<br /> fffff99f9fff9ff99f9f9fffffffffffffffffffffffffff<br /> f9ff9f9f9ffff9ff9f9f9fffffffffcffffccfcfcfffffff<br /> f9ffff9f9f999f9f9f9f9fffffffffcfcfcfcfcfcfffffff<br /> f99f9ff9fffff9fff9f9ffffffffffccffccfffcffffffff<br /> ffffffffffff9fffffffffffffffffcfcffccfccffffffff<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> .0000000000000000000000000000000000000000000000.<br /> ..a.............................................<br /> .1111.......................111111111...........<br /> ................................................<br /> ...........22......................22...........<br /> ................................................<br /> ..........................33....33..........33..<br /> ................................................<br /> .......444444........................444444444..<br /> ................................................<br /> .......555555...................................<br /> ................................................<br /> .6666...........................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> L(v j) = sum i a ij w i<br /> Used to define matrix rep of a linear map<br /> L and a sub ij<br /> <br /> j<br /> <br /> i<br /> <br /> v_j and w_i<br /> These are basis vectors, emphasis on the relation between them<br /> v_j<br /> <br /> L<br /> <br /> key<br /> key<br /> <br /> <br /> <br /> <br /> note<br /> about this horizontal line notation<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=L_and_a_sub_ij L and a sub ij 2019-04-06T01:26:48Z <p>76.90.99.69:&#32;</p> <hr /> <div>&lt;ppimage&gt;<br /> 117777117117775777777777717777777777771777777777<br /> 177777717171775777777777177711177777777177777777<br /> 177177717111775711117777177117177777777177777777<br /> 177177717171775777777777177177171777177177777777<br /> 177117717117775777777777177111177777777177777777<br /> 177777717777775711111777717777171777171777777777<br /> 117777117111175777777777777777771171177777777777<br /> 777777777171775777777777777777777773777777777777<br /> 777777777111775777777777777777777777777777777777<br /> 777777777771775777777777777777777773777777777777<br /> 777777777777775777777777777777777733777777777777<br /> 5bbbbbbbbbbbb54555555711777777777377777777771777<br /> 777777777777775777777717777777777377777777771117<br /> 777777777777775777777117777777777377777777777717<br /> 777777777777775777777117777777777377777777777711<br /> 777777777777775777777177777777777377777777777771<br /> 777777777777775777777177777777777377777777777771<br /> 777777777777775777777177777777777377777777777771<br /> 777777777777775777777177777777777377777777777771<br /> 777777777777775777777177777777777377777777777771<br /> 777777777777775777777177777777777777777777777771<br /> 777777777777775777377177777777733377777777777771<br /> 777777777777775777777177777777337377777777777771<br /> 777777777777775777377133333337377377777773333371<br /> 777777777777775777377177777777333373777377777771<br /> 777777777777775777337177777777777377777777777771<br /> 777777777777775777777177777777777773777377777771<br /> 777777777777775777777177777777777373373377777771<br /> 777777777777775777777177777777777377777777777771<br /> 777777777777775777777117777777777377777777777711<br /> 777777777777775777777711177777777377777777777717<br /> 777777777777775777777771177777777377777777777117<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> alpha and beta<br /> what are these?<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Linear_Algebra Linear Algebra 2019-04-06T01:13:40Z <p>76.90.99.69:&#32;I don't think we can write a_{ij} in the title of a page</p> <hr /> <div>&lt;ppimage&gt;<br /> fffff99fffffff99fffff99999ffffffffffffffffffffff<br /> ff9ff9ffff9ffff9f999f9ffffff999fffffffffffffffff<br /> ff9ff9f99f9ffff9ffffff9fffff9f9ffffff99f9f9fffff<br /> ff9ff9ff9f9ffff9f999fff9ffff9f9fffffff9f9f9fffff<br /> ff99f9ff9f9f9ff9ffffff9fffff999f9fff9f9f9f9f9fff<br /> fffff99ff9ffff99fffff9ffff9fff9ffffffff9f9ffffff<br /> ffffffffffff9ffffffff99999ffffff9fff9fffffff9fff<br /> fffffffffff99fffffffffffff9fffff99f99fffffff99ff<br /> ffffffffffffffffffffffffff99ffffffffffffffffffff<br /> 7bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb7<br /> ff4fffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb77777777777777777777777bbbbbbbbb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777bb7777777777777777777777bb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777777777777777777bb7777bb7777777777bb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb777777777777777777777777bbbbbbbbb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb77777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb7777777777777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 000000000000000000000000000000000000000000000000<br /> fffff99f9fff9ff99f9f9fffffffffffffffffffffffffff<br /> f9ff9f9f9ffff9ff9f9f9fffffffffcffffccfcfcfffffff<br /> f9ffff9f9f999f9f9f9f9fffffffffcfcfcfcfcfcfffffff<br /> f99f9ff9fffff9fff9f9ffffffffffccffccfffcffffffff<br /> ffffffffffff9fffffffffffffffffcfcffccfccffffffff<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> .0000000000000000000000000000000000000000000000.<br /> ..a.............................................<br /> .1111.......................111111111...........<br /> ................................................<br /> ...........22......................22...........<br /> ................................................<br /> ..........................33....33..........33..<br /> ................................................<br /> .......444444........................444444444..<br /> ................................................<br /> .......555555...................................<br /> ................................................<br /> .6666...........................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> L(v_j) = \sum_i a_{ij} w_i<br /> Used to define matrix rep of a linear map<br /> L and a sub ij<br /> <br /> j<br /> <br /> i<br /> <br /> v_j and w_i<br /> These are basis vectors, emphasis on the relation between them<br /> v_j<br /> <br /> L<br /> <br /> key<br /> key<br /> <br /> <br /> <br /> <br /> note<br /> about this horizontal line notation<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Linear_Algebra Linear Algebra 2019-04-06T00:43:58Z <p>76.90.99.69:&#32;Should've been a main page for the linear algebra portal but instead wrote a page about the matrix representation of a linear map.</p> <hr /> <div>&lt;ppimage&gt;<br /> fffff99fffffff99fffff99999ffffffffffffffffffffff<br /> ff9ff9ffff9ffff9f999f9ffffff999fffffffffffffffff<br /> ff9ff9f99f9ffff9ffffff9fffff9f9ffffff99f9f9fffff<br /> ff9ff9ff9f9ffff9f999fff9ffff9f9fffffff9f9f9fffff<br /> ff99f9ff9f9f9ff9ffffff9fffff999f9fff9f9f9f9f9fff<br /> fffff99ff9ffff99fffff9ffff9fff9ffffffff9f9ffffff<br /> ffffffffffff9ffffffff99999ffffff9fff9fffffff9fff<br /> fffffffffff99fffffffffffff9fffff99f99fffffff99ff<br /> ffffffffffffffffffffffffff99ffffffffffffffffffff<br /> 7bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb7<br /> ff4fffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb77777777777777777777777bbbbbbbbb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777bb7777777777777777777777bb77777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 77777777777777777777777777bb7777bb7777777777bb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb777777777777777777777777bbbbbbbbb77<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7777777bbbbbb77777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 7bbbb7777777777777777777777777777777777777777777<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> ffffffffffffffffffffffffffffffffffffffffffffffff<br /> 000000000000000000000000000000000000000000000000<br /> fffff99f9fff9ff99f9f9fffffffffffffffffffffffffff<br /> f9ff9f9f9ffff9ff9f9f9fffffffffcffffccfcfcfffffff<br /> f9ffff9f9f999f9f9f9f9fffffffffcfcfcfcfcfcfffffff<br /> f99f9ff9fffff9fff9f9ffffffffffccffccfffcffffffff<br /> ffffffffffff9fffffffffffffffffcfcffccfccffffffff<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> .0000000000000000000000000000000000000000000000.<br /> ..a.............................................<br /> .1111.......................111111111...........<br /> ................................................<br /> ...........22......................22...........<br /> ................................................<br /> ..........................33....33..........33..<br /> ................................................<br /> .......444444........................444444444..<br /> ................................................<br /> .......555555...................................<br /> ................................................<br /> .6666...........................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> ..............................77777777777.......<br /> L(v_j) = \sum_i a_{ij} w_i<br /> Used to define matrix rep of a linear map<br /> L and a_{ij}<br /> <br /> j<br /> <br /> i<br /> <br /> v_j and w_i<br /> These are basis vectors, emphasis on the relation between them<br /> v_j<br /> <br /> L<br /> <br /> key<br /> key<br /> <br /> <br /> <br /> <br /> note<br /> about this horizontal line notation<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=PlayPen:Projects2 PlayPen:Projects2 2019-04-05T23:02:35Z <p>76.90.99.69:&#32;Added a new project for linear algebra</p> <hr /> <div>&lt;ppimage&gt;<br /> 011111111111111111111111111111111111111111111110<br /> 118888888888888888888888888888888888888888888811<br /> 188880008888888800088888880008888888000888888881<br /> 188803c3088888800100888880ee208888806dd088888881<br /> 18880ccc0800008010108000808ee0800080dd4080008881<br /> 188807770888888001008888803ee0888880baa088888881<br /> 188880008888888800088888880008888888000888888881<br /> 188888888888888888888888888888888888888888888881<br /> 188888888888888888888888888888888888888888888881<br /> 188880008888888800088888880008888888000888888881<br /> 188806660888888022208888800990888880eee088888881<br /> 188806c60800008002008000809090800080ddd080008881<br /> 188806660888888002008888809900888880999088888881<br /> 188880008888888800088888880008888888000888888881<br /> 188888888888888888888888888888888888888888888881<br /> 188888888888888888888888888888888888888888888881<br /> 188880008888888800088888880008888888000888888881<br /> 18880d4d0888888033308888803030888880d11088888881<br /> 1888043408000080bbb08000803330800080d11080008881<br /> 188804440888888099908888800300888880dd1088888881<br /> 188880008888888800088888880008888888000888888881<br /> 188888888888888888888888888888888888888888888881<br /> 188888888888888888888888888888888888888888888881<br /> 188888838888888800088888880008888888888838888881<br /> 188888338888888011108888801110888888888833888881<br /> 188883333333388011108000801110800083333333388881<br /> 188833333333388011108888801110888883333333338881<br /> 1888f33333333888000888888800088888833333333f8881<br /> 18888f33fffff8888888888888888888888fffff33f88881<br /> 188888f3f888888888888888888888888888888f3f888881<br /> 1188888f88888888888888888888888888888888f8888811<br /> 011111111111111111111111111111111111111111111110<br /> ................................................<br /> ................................................<br /> ................................................<br /> .....000........111.......222.......333.........<br /> .....000........111.......222.......333.........<br /> .....000........111.......222.......333.........<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> .....444........555.......666.......777.........<br /> .....444........555.......666.......777.........<br /> .....444........555.......666.......777.........<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> .....888........999.......bbb.......aaa.........<br /> .....888........999.......bbb.......aaa.........<br /> .....888........999.......bbb.......aaa.........<br /> ................................................<br /> ................................................<br /> ................................................<br /> .......e................................f.......<br /> ......ee................................ff......<br /> .....eeeeeeee......................ffffffff.....<br /> ....eeeeeeeee......................fffffffff....<br /> .....eeeeeeee......................ffffffff.....<br /> ......ee................................ff......<br /> .......e................................f.......<br /> ................................................<br /> ................................................<br /> ExplosionMan<br /> Explode stuff with Explosion man!<br /> Tictactoe<br /> Play the classic game &quot;Tic-Tac-Toe&quot; with &quot;computer&quot; in PlayPen!\nIt's incredible and super fun!\nRecommended by Stick Figure\n10/25/2011 12:25 (24h format, UTC time)<br /> User:Creativo-golf123<br /> Creativo-golf123 is a creative colaborator! \n As you can see, he added \n some wings and a portal to \n Weird World in the main page, wow!<br /> Weird World<br /> Go to Weird World, is weird but fun! \nRecommended by Creativo-golf123<br /> Welcome To Space!<br /> Portal 2<br /> TimeTon<br /> SkipperThePenguin100's TimeTon adventure project, it's a adventure game which takes on space.<br /> WorldofGoo<br /> Come check out World of Goo, by Darkus2014!<br /> RuinedWorld<br /> Explore a Ruined World<br /> LALALAND<br /> Come to LALALAND, made by Darkus2014's friend!<br /> Diehard<br /> 1%<br /> Linear Algebra<br /> Exploratory medium for linear algebra<br /> UndertaleStartRoom<br /> Let's create Undertale within PlayPen!<br /> <br /> <br /> <br /> <br /> PlayPen:Projects<br /> Previous Page<br /> PlayPen:Projects3<br /> Next Page<br /> &lt;/ppimage&gt;</div> 76.90.99.69 http://playpen.farbs.org/index.php?title=Hide_it_in_the_tree Hide it in the tree 2019-04-05T22:56:14Z <p>76.90.99.69:&#32;Linear Algebra</p> <hr /> <div>&lt;ppimage&gt;<br /> eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee<br /> ee11e111eeeeee111eeeeee11111111eee1ee111eeeeeeee<br /> 1111e1eeeeeeeeee1eeeeee1eeeeee1ee11ee1eeeeeeeeee<br /> 1ee1e1ee11ee11ee1eeeeee1111eeeeee1eee1eeeeeeeeee<br /> 1ee1e1eee1111eee1eeeeeeeee1eeeeee1eee1eeeeeeeeee<br /> 1111e1eeee11eeee111111e1111eeeeee11ee1eeeeeeeeee<br /> 1e11e1eee111eeee1eeeeee11eeeeeee111ee1eeeeeeeeee<br /> 1ee1e1ee11e11eee1e11111e1eeeee1e1e11e1eeeeeeeeee<br /> 1eeee1ee1eee1eee1eeeeeee1e11111e1ee1e1eeeeeeeeee<br /> eeeee11eeeeeeeee1eeeeeee111eeeee1111e1111eeeeeee<br /> eeeeeeeeeeeeee111eeeeeeeeeeeeeee1ee1ee1eeeeeeeee<br /> eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee1eeeeeeeee<br /> eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee111eeeeeee<br /> eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee<br /> 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................................................<br /> .........00.....................................<br /> ........00000...................................<br /> .......0000000..................................<br /> .......0000000..................................<br /> .......0000000..................................<br /> .......0000000..................................<br /> .......000000...................................<br /> ........00000...................................<br /> ..........00....................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> ................................................<br /> Destination page<br /> x in terms of <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/ppimage&gt;</div> 76.90.99.69