Gaussian Elimination Does a simple Gaussian elimination works on all matrices? Or is there cases where it doesn't work?
My guess is yes, it works on all kinds of matrices, but somehow I remember my teacher points out that it doesn't works on all matrices. But I'm not sure, because I have been given alot of methods, and maybe I have mixed it all up.

Gaussian elimination without pivoting works only for matrices all whose leading principal minors are non-zero. See http://en.wikipedia.org/wiki/LU_decomposition#Existence_and_uniqueness.
