HELP - Difference between Guassian Elimination and Augmented?

Does it really make a difference?

I actually don't know what the difference is...but a quick Wikipedia check should answer the question:

"Elementary row operations are used to reduce a matrix to what is called triangular form (in numerical analysis) or row echelon form (in abstract algebra). Gauss?Jordan elimination, an extension of this algorithm, reduces the matrix further to diagonal form, which is also known as reduced row echelon form."

Which means I don't see that there is ANY differene in using an augmented matrix and Gaussian Elimination (actually I think Gaussian Elimination is the name given for how you solve the "augmented matrix problem").

Gaussian: only get upper triangular form (meaning you have 0's for everything below the diagonal but not necessarily above).

Gaus-Jordan: get reduced echelon form, meaning you have ONLY diagonal entries (i.e zeros are everywhere except on the diagonals...for which there should be NO zeros otherwise this matrix is singular).