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5.35.7 Row reduction to echelon form in ℤ/pℤ: Rref

In Xcas mode, Rref is simply the inert form of rref; namely, it returns rref without evaluating it. (See Section 5.56.3.) In Maple mode, the Rref command can additionally be used in conjunction with mod to find the reduced row echelon form of a matrix whose elements are in ℤ/pℤ.

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%132%13

−4
%13
3%13

−3
%13
0%13








To actually get the reduced echelon form, you can enter:
Input:

eval(ans())

Output:



1%130%133%13
0%131%133%13


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

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

Output:



103
013


and again conclude that x=3%13 and y=3%13.


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