( a 11 x + a 12 y ) mod 8 = b 1 ( a 21 x + a 22 y ) mod 8 = b 2 In the case of simple equations without modulo, the solution of A x = b is x = A − 1 b, but how to handle this modulo?

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(      a      11    x  +      a      12    y  )    mod      8  =      b    1    (      a      21    x  +      a      22    y  )    mod      8  =      b    2  In the case of simple equations without modulo, the solution of   A  x  =  b is   x  =      A          −      1        b, but how to handle this modulo?

svirajueh · Accepted Answer

You can do Gauss-Jordan elimination performing operations modulo 8. Just be mindful that &quot;division&quot; is only defined for odd integers (you are really multiplying by the inverse modulo 8).

lobht98 · Accepted Answer

You can apply Cramer&#039;s rule if the determinant is odd (so invertible mod 8). For an introduction to linear algebra over commutative rings see Wm. C. Brown: Matrices over commutative rings.

( a 11 </msub> x + a 12 </msub> y ) <mspace

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