### 2.52.2 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 :

⎧ ⎨ ⎩ |
3x + y | = | −2
3x +2y | = | 2

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).