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Show that for each nonsingular n x n matrix A there exists a permutation matrix P...

Show that for each nonsingular n x n matrix A there exists a permutation matrix P such that P A has an LR decomposition.

[note: A factorization of a matrix A into a product A=LR of a lower (left) triangular matrix L and an upper (right) triangular matrix R is called an LR decomposition of A.]

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