a) Let x be feasible but not a basic feasible solution for Ax = b, x > 0. Prove that the columns of A corresponding to the nonzero entries of x are linearly dependent. b) Let x be a feasible point of X = {x Rn: Ax = b, x > 0} that is not an extreme point. Prove that there exists a vector p Rn, p 0 such that Ap = 0 pi = 0 if xi = 0. (Hint: Use the result from part a).)