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Unformatted text preview: A is A = LU where L is a lower triangular matrix and U is upper triangular. This was done by multiplying elementary matrices times A until the result is an upper triangular matrix U, E k E k1 E 1 A = U. Then we multiply the inverses of the elementary matrices to solve for A, A = E1 1 E1 1 E1 k U. It turns out that L = E1 1 E1 1 E1 k is a lower triangular matrix. This is because the elementary row operations we used to nd a row equivalent upper triangular matrix to A are lower triangular and the product of lower triangular matrices is lower triangular and the inverse of a lower triangular matrix is lower triangular. 1...
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 Winter '08
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 Math, Matrices

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