I was watching MIT Linear Algebra lectures 3-Multiplication and Inverses, and 4-Factorization into A=LU and 10 minutes into lecture 4...the tape quit! Damn! Factoring a matrix A into the product of a lower triangular matrix L and an upper triangular matrix U is a pretty useful thing to know how to do. It makes calculating things like trace, determinants, and inverses of A really easy...
Alas...it is a good thing that I already new how to do the factorization...but here is a link to the video lecture that will work...the link takes you to a series of written notes based on the MIT lecture series which is also quite useful...
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