### 5.56.2 Gauss reduction of a matrix : ref

ref is used to solve a linear system of equations written in
matrix form:

A*X=B

The argument of ref is the augmented matrix of the system
(the matrix obtained by augmenting the matrix A to the right with
the column vector B).

The result is a matrix [A1,B1] where A1 has zeros
under its principal diagonal, and the solutions of:

A1*X=B1

are the same as the solutions of:

A*X=B

For example, solve the system :

Input :

ref([[3,1,-2],[3,2,2]])

Output :

[[1,1/3,-2/3],[0,1,4]]

Hence the solution is y=4 (last row) and x=−2 (substitute y
in the first row).