Let p = {x ∈ rn : ax = b, x ≥ 0} be a nonempty polyhedron, and let m be the dimension of the vector b. we call xj a null variable if xj = 0 for all x ∈ p. suppose there exists some p ∈ rm for which p′a ≥ 0, p′b = 0, and such that the jth component of p′a is positive. prove that xj is a null variable.