Question: Please help me the problem: Problem 4. Let A be an n x n square matrix. 1. Show that A is invertible if and only

Please help me the problem:

Problem 4. Let A be an n x n square matrix. 1. Show that A is invertible if and only if has n strictly positive singular values i.e., oi > 0 for all i = 1, ..., n. 2. If the SVD of A is A = UEV* and A is invertible, what is the SVD of A-!? 3. Show that if A is invertible then A | = , where min is the smallest singular value of A and |.|| is the matrix Euclidean norm

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