My book is awful and I need clarification on a few things regarding LU factorization:
-If I am trying to express matrix A as a product of its upper triangular matrix (U) and the lower triangular matrix (L). I understand that I should find U first by Gauss-Jordon elimination method. But does U have to have all 1s in the diagonal or is U found once you have all zeros below the diagonal regardless of whether you have all ones in the diagonal or not?
-Once you have U, to get L, I understand that you need to multiply the inverses of all elementary matrices used to get U. But I'm unclear on the quick process of getting the inverses of the elementary matrices of a 3x3 square matrix (without having to go through Gauss Jordon elimination method again on each one).