Solved: TF. In parts (a)(e) determine whether the statement is true or false, and

Chapter 9, Problem TF

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TF. In parts (a)(e) determine whether the statement is true or false, and justify your answer. (a) Every square matrix has an LU-decomposition. (b) If a square matrix A is row equivalent to an upper triangular matrix U, then A has an LU-decomposition. (c) IfL1, L2,...,Lk are n n lower triangular matrices, then the product L1L2 Lk is lower triangular. (d) If an invertible matrix A has an LU-decomposition, then A has a unique LDU-decomposition. (e) Every square matrix has a P LU-decomposition.

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