a) 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, what can you say aboutEAET?
b) Use step a) to prove that any symmetric matrix that can berow reduced without swaps can be written as A = LDLT
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 = LDLT(U = LT)
PLEASE HELP ME WITH THIS QUESTION. I HAVE BEEN SPENDING HOURSSOLVING IT AND I GOT STUCK. THANK YOU VERY MUCH FOR YOUR HELP!
