Consistency of a linear system of inequalities (Q1061454)

We show that a consistency check of a linear system of inequalities Ax\(\leq b\) reduces to check whether Qb\(\geq 0\) for a certain matrix Q. It is a direct consequence of the Farkas-Minkowski theorem. Thus, when one has to check consistency for different values of b, one need not run a numerical algorithm for each b.