Systems of linear equations

1. Sep 19, 2007

buzzmath

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?

Last edited: Sep 19, 2007