12. (General positive state prices result o) The following is a general result from matrix. theory: Let A be an m x matrix Suppose that the equation Ax = p can achieve no p 0 except p=0. Then there is a vector y >0 with A' y = 0 Use this result to show that if there is no arbitrage, there are positive state prices; that is, prove the positive state price theorem in Section 99 [Hint If there are S states and N securities, let A be an appropriate (S+1) x N matrix ]