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10.10.7  Row reduction to echelon form in ℤ/p

In Xcas mode, Rref is simply the inert form of rref; namely, it returns rref without evaluating it (see Section 14.7.3). 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+2y=9,
      3x+10y=0.

Input in Xcas mode:

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







      1%132%13

−4
%13
      3%13

−3
%13
0%13








          

To actually get the reduced echelon form, enter:

eval(ans())
     


    1%130%133%13
    0%131%133%13


          

Input in Maple mode:

Rref([[1,2,9],[3,10,0]] mod 13)
     


103
013


          

In both cases you conclude that x=3%13 and y=3%13.


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