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Gauss reduction of a matrix : ref

ref is used to solve a linear system of equations written in matrix form:
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:
are the same as the solutions of:

For example, solve the system :

$\displaystyle \left\{\vphantom{
\begin{array}{lcr} 3x + y & = &-2 \\  3x +2y & =& 2 \end{array}}\right.$$\displaystyle \begin{array}{lcr} 3x + y & = &-2 \\  3x +2y & =& 2 \end{array}$

Input :
Output :
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