A System With Two Free Variables

Consider the following 4 by 5 matrix, G2, which represents the augmented matrix for a system of 4 equations in 4 variables:

> G2:=matrix(4,5,[4,2,-5,-5,-3,-1,6,-5,-1,2,-5,4,0,4,5,9,-2,-5,-9,-8]);

Let's find the Row-Echelon form of G2:

> gausselim(G2);

There are no pivots in columns 3 and 4, indicating that the third and fourth variables, x_3 and x_4, are free. If we use the Gauss-Jordan Method, we'll find the other two variables in terms of the two free variables:

> gaussjord(G2);

>