1. The problem statement, all variables and given/known data A is an nxn symmetric and positive definate matrix. Show that A admits a factorization A=LU In other words, no zero pivot is encountered during the elimination process. 2. Relevant equations cholesky factorization 3. The attempt at a solution I think all I have to show is that after 1 step in G.E. a(1,1) does not equal 0 and that the first row is the same as the first row in A and the first column is all zeros except for a(1,1). then show that the remaining (n-1)x(n-1) matrix is symmetric and positive definate. I showed that a(1,1) is not zero but I don't know how to prove the (n-1)x(n-1) matrix is positive definate and symmetric. any help or suggestions?