8. Assume A is a square matrix with a nonzero determinant, L'U' = LU = A...

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8. Assume A is a square matrix with a nonzero determinant, L'U' = LU = A where L and L' are lower triangular matrices and U and U' are upper triangular matrices. Show there exists a diagonal matrix D such that L=L'D and U = DU'. 8. Assume A is a square matrix with a nonzero determinant, L'U' = LU = A where L and L' are lower triangular matrices and U and U' are upper triangular matrices. Show there exists a diagonal matrix D such that L=L'D and U = DU'.