[Solution] Suppose that A ∈ R^n * n is invertible. Show that if there exists a factorization A=L U where L is lower triangular with ones on the diagonal
Question: Suppose that \(A \in \mathbb{R}^{n \times n}\) is invertible. Show that if there exists a factorization \(A=L U\) where \(L\) is lower triangular with ones on the diagonal and \(U\) is upper triangular, then there is a unique such factorization. (Hint: what can you say about the inverse of a triangular matrix? What about the inverse of a triangular matrix with ones on the diagonal?)
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