http://img24.imageshack.us/img24/7783/44818829.gif

So, in the answer I don't understand how they obtained

I don't think this "L" here is the lower triangular matrix used in the LU factorization of A. Because I followed the LU decomposition algorithm and ended up with

So where did they get that matrix from? Any explanation is very much appreciated.

PS: I'm sorry this was meant to go to the Linear Algebra section! :(