Problem 4 (4+6+10=20 points) Let A E Rmxn, m > n, have an SVD A = UEV' with orthogonal matrix U = (u1, ..., Um) E mxm of left singular vectors, orthogonal matrix V = (v1, . .., Vn) E Rx" of right singular vectors and diagonal matrix E E Rmxn with singular values o1 2 02 2 ... 2 On 2 0. (a) (4 points) Let Q E Rmxm be orthogonal. What are the singular values of QA? Compute an SVD of QA. What are left singular vectors and what are right singular vectors? (b) (6 points) Let t E R. What are the singular values of tA? Compute an SVD of tA. What are left singular vectors and what are right singular vectors? (c) (5 points) Assume that BE RXk, n > k, has an SVD B = VEX' with orthogonal matrix V as before, orthogonal matrix X E RkXk and diagonal matrix E E Rxk with singular values $1 2 52 2 ... 2 Ex 2 0. What are the singular values of AB? Compute an SVD of AB. What are left singular vectors and what are right singular vectors