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## 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