### 5.33.7 Row reduction to echelon form in ℤ/pℤ : Rref

Rref is the inert form of rref.
Rref returns rref without evaluation. It is used in conjunction with mod in Maple syntax mode to find the row reduction to echelon form of a matrix with coefficients in ℤ/pℤ (see also 5.54.3).
Example, solve in ℤ/13ℤ

⎧ ⎨ ⎩ |
x + 2 · y | = | 9
3 · x +10 · y | = | 0

Input in Xcas mode :

Rref([[1,2,9] mod 13,[3,10,0] mod 13])

Output :

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

you need to eval(ans()) to get :

[[1%13,0%13,3%13],[0%13,1%13,3%13]]

and conclude that x=3%13 and y=3%13.
Input in Maple mode :

Rref([[1,2,9],[3,10,0],[3,11,1]]) mod 13

Output :

[[1,0,0],[0,1,0],[0,0,1]]