** suivant:** Gauss-Jordan reduction: rref gaussjord
** monter:** Linear systems
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##

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).

giac documentation written by Renée De Graeve and Bernard Parisse