A System With One Free Variable

Consider the following 4 by 5 matrix, G1, which represents the augmented matrix for a system of 4 equations in 4 variables:

> G1:=matrix(4,5,[4,2,-5,-5,-3,4,-3,-2,-5,2,-5,4,0,4,5,8,-1,-7,-10,-1]);

Let's find the Row-Echelon form of G1:

> gausselim(G1);

There is no pivot in column 4, indicating that the fourth variable, x_4, is free. If we use the Gauss-Jordan Method, we'll find the other three variables in terms of the free variable:

> gaussjord(G1);

>