i am solving some linear equation system in finite field with characteristic 2, when i apply LinearSolve function to the equation system Mathematica tells me that the system has no solution. for example:
my equation system is x1+x2==1,x3+x4==1,x1+x4==0,x2+x3==0,
Out:LinearSolve::nosol: Linear equation encountered that has no solution. >>
but in F2 there exists a solution for the system that is 0,1,1,0.
can any one tell me how to do that? or how can i just check the consistency of this kind of equation system in F2.