** suivant:** Construction of a Galois
** monter:** Computing in /p or
** précédent:** Inverse of a matrix
** Table des matières**
** Index**

##

Row reduction to echelon form in
/*p* : `rref`

`rref` find the row reduction to echelon form of
a matrix with coefficients in
/*p*.
This may be used
to solve a linear system of equations with coefficients in
/*p*,
by rewriting it in matrix form (see also 1.52.3) :

`A*X=B`

`rref` takes as argument the augmented matrix
of the system (the matrix obtained by augmenting matrix `A` to the
right with the column vector `B`).

`rref` returns a matrix `[A1,B1]` : `A1` has 1 on
it's principal diagonal, and zeros outside, and the
solutions in
/*p*, of :
`A1*X=B1`

are the same as the solutions of:
`A*X=B`

Example, solve in
/13

Input :
`rref([[1, 2, 9]%13,[3,10,0]%13])`

Or :
`rref([[1, 2, 9],[3,10,0]])%13`

Output :
`[[1%13,0%13,3%13],[0%13,1%13,3%13]]`

hence `x=3%13` and `y=3%13`.

giac documentation written by Renée De Graeve and Bernard Parisse