Let z1 be a q x 61 matrix and z2 a q X 62 matrix such that the columns of 2 = (21 22) are linearly independent. (a) Show that the columns of z1 are linearly independent. (b) Suppose C(z1) _ C(z2). Explain why 2521 = 0. (c) Let Y be an n x q matrix, and define Yz = Yz(z'z) -1 Y21 = Yz1(2121) -1