Let p = {? ? rn . ax = b, x > 0} be a nonempty polyhedron, and let m be the (a) suppose there exists some p e rt for which p'a 2 0, p'b 0, and such that the jth (b) prove the converse of (5a): ifay is a null variable, then there exists some p e rm for (c) if ay is not a null variable, then by definition there exists some y ? p for which 0. dimension of the vector ó. we call dz a null variable if = 0 for all x e p component of p'a is positive. prove that xj is a null variable which p'a use the results in parts (5a) and (5b) to prove that there exists x ? p and p 0, p'b 0, and such that the jth component of p'a is positive. rm such that: