Originally Posted by
ANDS! Gaussian elemination is just a process of reducing systems of equations so that you can eventually start to back substitute values into previous equations. Row echelon form simply means the first non-zero entry of a row is to the right of the first non zero entry of the row above it. One is a process, the other is a representation of a matrix. They are not exclusive. Reduced row echelon form simply means you continue Gaussian elimination beyond simply putting it into row echelon form.