Opera\303\247\303\265es elementares nas linhas sem introduzir as fra\303\247\303\265es. Xhumga Bernard Amateur en Math\303\251matique et en langage C. D\303\251butant sur maple 15. Maple Cloud : mathc

No in\303\255cio, tentei resolver um sistema de equa\303\247\303\265es sem introduzir as fra\303\247\303\265es. Em segundo lugar, tentei ver se poder\303\255amos fazer esse trabalho automaticamente.

restart: with(Student[LinearAlgebra]): randomize():

restart: with(Student[LinearAlgebra]): A := Matrix(3,4, [ -2, 31,-91,-50, 66,-53,-96,-29, 57, 74,-23, 58]): M := A;

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

M := MultiplyRow(M, 2, -2): M := MultiplyRow(M, 3, -2): M := AddRows(M,2, 1,-66): M := AddRows(M,3, 1,-57): M;

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

M := MultiplyRow(M, 2, -1/(igcd(1940, 6198, 3358))): M := MultiplyRow(M, 3, -1/(igcd(1915, 5233, 2734))): M;

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

M := MultiplyRow(M, 3, 970): M := AddRows(M,3, 2,-1915): M;

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

M := MultiplyRow(M, 3, 1/(igcd(858575, 563305))): M;

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

M := MultiplyRow(M, 2, 171715): M := MultiplyRow(M, 1, 171715): M := AddRows(M,2, 3,3099): M := AddRows(M,1, 3,91): M;

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

M := MultiplyRow(M, 2, 1/(igcd(166563550, 60826954))): M := MultiplyRow(M, 1, 1/(igcd(343430, 5323165,1666401))): M;

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

M := MultiplyRow(M, 1, 858575 ): M := AddRows(M, 1, 2,-5323165 ): M;

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

M := MultiplyRow(M, 1, -1/(igcd(294860412250, 238300238690))): M;

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

ReducedRowEchelonForm(A);

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

restart: with(Student[LinearAlgebra]): A := Matrix(3,4, [ -2, 31,-91,-50, 66,-53,-96,-29, 57, 99,-23, 58]): M := A;

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

M11 := M[1,1]: M21 := M[2,1]: M31 := M[3,1]: M := MultiplyRow(M, 2, M11): M := MultiplyRow(M, 3, M11): M := AddRows(M,2, 1,-M21): M := AddRows(M,3, 1,-M31): M;

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

M22 := M[2,2]: M32 := M[3,2]: M := MultiplyRow(M, 3, M22): M := AddRows(M,3, 2,-M32): M;

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

M33 := M[3,3]: M23 := M[2,3]: M13 := M[1,3]: M := MultiplyRow(M, 2, M33): M := MultiplyRow(M, 1, M33): M := AddRows(M,2, 3,-M23): M := AddRows(M,1, 3,-M13): M;

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

M22 := M[2,2]: M12 := M[1,2]: M := MultiplyRow(M, 1, M22): M := AddRows(M, 1, 2,-M12): M;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWFjdGlvbkdGJDYlLUkobWZlbmNlZEdGJDYoLUYjNiUtSSdtdGFibGVHRiQ2Ny1JJG10ckdGJDYpLUkkbXRkR0YkNigtSSNtbkdGJDYkUTIxNTk0MjY1NTAwNTcwMDAwMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lKXJvd2FsaWduR1EhRicvJSxjb2x1bW5hbGlnbkdGRS8lK2dyb3VwYWxpZ25HRkUvJShyb3dzcGFuR1EiMUYnLyUrY29sdW1uc3BhbkdGTC1GOjYoLUY9NiRRIjBGJ0ZARkNGRkZIRkpGTUZPLUY6NigtRj02JFEyMTE3NjQ1MjQwMzI0NjQwMDBGJ0ZARkNGRkZIRkpGTUZDRkZGSC1GNzYpRk8tRjo2KC1GIzYlLUkjbW9HRiQ2LVEqJnVtaW51czA7RidGQC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGX28vJSlzdHJldGNoeUdGX28vJSpzeW1tZXRyaWNHRl9vLyUobGFyZ2VvcEdGX28vJS5tb3ZhYmxlbGltaXRzR0Zfby8lJ2FjY2VudEdGX28vJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZecC1GPTYkUSszOTMyNDc3MDAwRidGQEZARkNGRkZIRkpGTUZPLUY6NigtRiM2JUZpbi1GPTYkUSsxMjE2NTM5MDgwRidGQEZARkNGRkZIRkpGTUZDRkZGSC1GNzYpRk9GTy1GOjYoLUY9NiRRKDIwMjcwNTBGJ0ZARkNGRkZIRkpGTS1GOjYoLUY9NiRRKDEyOTQ1MTBGJ0ZARkNGRkZIRkpGTUZDRkZGSC8lJmFsaWduR1ElYXhpc0YnL0ZEUSliYXNlbGluZUYnL0ZHUSZyaWdodEYnL0ZJUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdRJXRydWVGJy8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRmVyLyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRmBzLyUmZnJhbWVHRmBzLyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGX28vJS1lcXVhbGNvbHVtbnNHRl9vLyUtZGlzcGxheXN0eWxlR0Zfby8lJXNpZGVHRl1yLyUwbWlubGFiZWxzcGFjaW5nR0Zdcy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGQEZAL0krbXNlbWFudGljc0dGJFEnTWF0cml4RicvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGZXQvJSthY3Rpb250eXBlR1EucnRhYmxlYWRkcmVzc0YnLyUpcnRhYmxlaWRHUSk2MDE4NzAwNEYnRmJ0RkA=

M := MultiplyRow(M, 1,1/(igcd(M[1,1], M[1,4]))): M := MultiplyRow(M, 2,1/(igcd(M[2,2], M[2,4]))): M := MultiplyRow(M, 3,1/(igcd(M[3,3], M[3,4])));

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

ReducedRowEchelonForm(A);

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restart: with(Student[LinearAlgebra]): randomize(): A := RandomMatrix(3, 4); M := A:

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

M11 := M[1,1]: M21 := M[2,1]: M31 := M[3,1]: M := MultiplyRow(M, 2, M11): M := MultiplyRow(M, 3, M11): M := AddRows(M,2, 1,-M21): M := AddRows(M,3, 1,-M31): M;

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

M22 := M[2,2]: M32 := M[3,2]: M := MultiplyRow(M, 3, M22): M := AddRows(M,3, 2,-M32): M;

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M33 := M[3,3]: M23 := M[2,3]: M13 := M[1,3]: M := MultiplyRow(M, 2, M33): M := MultiplyRow(M, 1, M33): M := AddRows(M,2, 3,-M23): M := AddRows(M,1, 3,-M13): M;

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M22 := M[2,2]: M12 := M[1,2]: M := MultiplyRow(M, 1, M22): M := AddRows(M, 1, 2,-M12): M;

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M := MultiplyRow(M, 1,1/(igcd(M[1,1], M[1,4]))): M := MultiplyRow(M, 2,1/(igcd(M[2,2], M[2,4]))): M := MultiplyRow(M, 3,1/(igcd(M[3,3], M[3,4])));

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ReducedRowEchelonForm(A);

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Um dos erros que cometi foi o esquecimento de salvar os valores na matriz de trabalho antes de realizar os primeiros c\303\241lculos. Ruim : > M := MultiplyRow(M, 2, M[1,1]): > M := MultiplyRow(M, 3, M[1,1]): > > M := AddRows(M,2, 1,-M[2,1]): > M := AddRows(M,3, 1,-M[3,1]): Bom : > M11 := M[1,1]: > M21 := M[2,1]: > M31 := M[3,1]: > > M := MultiplyRow(M, 2, M11): > M := MultiplyRow(M, 3, M11): > > M := AddRows(M,2, 1,-M21): > M := AddRows(M,3, 1,-M31): Por qu\303\252 ? As opera\303\247\303\265es de linha modificam os valores da matriz inicial. Portanto, \303\251 necess\303\241rio memorizar esses valores antes de qualquer trabalho.