a) Suppose that A = AT can be row reduced without row swaps. If E is...

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Advance Math

a) Suppose that A = A^T can be row reduced without rowswaps. If E is an elementary matrix such that EA has zero as asecond entry in the first column, what can you say aboutEAE^T?
b) Use step a) to prove that any symmetric matrix that can berow reduced without swaps can be written as A = LDL^T
P.s: L is the lower triangular matrix whose diagonal containsonly 1. D is a diagonal matrix whose diagonal contains the pivotsof A. Originally, the triangular factorization of A is A = LDU (Uis the upper triangular whose diagonal contains only 1), but sinceA is a symmetric matrix, it can be rewritten as A = LDL^T(U = L^T)
PLEASE HELP ME WITH THIS QUESTION. I HAVE BEEN SPENDING HOURSSOLVING IT AND I GOT STUCK. THANK YOU VERY MUCH FOR YOUR HELP!

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Suppose that A AT can be row reduced without rowswaps If E is an elementary matrix such that EA has zero as asecond entry in the first column then EA ET has boththe entries the second entry in the first row and the second entryin the first column will be zero See Answer

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