3. Prove that the Mahalanobis distance is metric if M is symmetric positive definite. That is, show that dm(x, y) = (x y) M(x y) satisfies the following conditions. (M1) d(x, y) 0 for (M2) d(x,y) = 0 < x = y (M3) d(x,y) = d(y,x) (M4) d(x,y) d(x, z) + d(z, y)