We will define some functions to create elementary matrices to do row reduction.
Eswap(n,i,j0 creates an $n\times n$ matrix to swap rows $i$ and $j$
Escale(n,i,c) creates a matrix to multiply row $i$ by $c$
Esub(n,i,j,c) subtracts $c*$Row $i$ from Row $j$
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[ 1 0 0 0 0] [ 0 1 0 0 0] [-7 0 1 0 0] [ 0 0 0 1 0] [ 0 0 0 0 1] [ 1 0 0 0 0] [ 0 1 0 0 0] [-7 0 1 0 0] [ 0 0 0 1 0] [ 0 0 0 0 1] |
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The following is the matrix to row reduce in Exam 1.
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[1 0 0] [0 1 0] [0 0 1] [1 0 0] [0 1 0] [0 0 1] |
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[ 1 0 0 -1/264 7/396 -5/792] [ 0 1 0 59/1848 -17/2772 295/5544] [ 0 0 1 37/924 5/1386 -739/2772] [ 1 0 0 -1/264 7/396 -5/792] [ 0 1 0 59/1848 -17/2772 295/5544] [ 0 0 1 37/924 5/1386 -739/2772] |
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[ 1 0 0 7/85 -1/15 7/51] [ 0 1 0 1/85 2/15 1/51] [ 0 0 1 6/85 2/15 -11/51] [ 1 0 0 7/85 -1/15 7/51] [ 0 1 0 1/85 2/15 1/51] [ 0 0 1 6/85 2/15 -11/51] |
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[ 1 0 1 0 -2/9 7/18] [ 0 1 1 0 1/9 1/18] [ 0 0 0 1 17/9 -55/18] [ 1 0 1 0 -2/9 7/18] [ 0 1 1 0 1/9 1/18] [ 0 0 0 1 17/9 -55/18] |
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[ 1 0 7/11 0 -6/55 7/55] [ 0 1 1/11 0 7/55 1/55] [ 0 0 0 1 1 -1] [ 1 0 7/11 0 -6/55 7/55] [ 0 1 1/11 0 7/55 1/55] [ 0 0 0 1 1 -1] |
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