I'm still confused about L U matrix factorization. I'm trying to understand how to do it and why doing so is valuable. Would elementary row operations to solve Ax=b be easier? I'm not in any class. I am looking in the Larson & Edwards Linear Algebra book. Chapter 2. I have trouble following the different elementary matrices that are used in finding the U and the L matrices. I am confused about how certain numbers are selected to be part of each elementary matrix, the ones that have mostly the 1's along the main diagonal, and that some in the main diagonal are not 1's. Then, there is some other matrix containing other elements that came from using the elementary matrices.