Now that we know RREF and REF for a given matrix, and how we can apply elementary row operations, the next step is to develop a procedure to obtain either RREF or REF from a starting matrix.
The Gaussian Elimination procedure I will show you here will reduce a given matrix to its Row Echelon Form. This elimination procedure is advantageous when we have small linear systems in which we can use backwards-substitution to solve (more on this later). It's downside? It is not a unique form. This means that we could get two different REFs for a given starting matrix!
