a) Write a MATLAB program that constructs a 50 50 matrix A = U *S * V 1 , where U and V are random orthogonal matrices and S is a diagonal matrix whose diagonal entries are random uniformly distributed numbers [0, 1], sorted into non increasing order. Have your program compute [U2, S2, V2] svd(A) and the norms of U - U2 V - V2, and S -S2 and A -U2 *S2 *V2. Do this for five matrices A and comment on the results. (Hint: Plots of diag(U 2 *U) and diag(V 2 * V ) (b) Fix the signs in your computed SVD so that the difficulties of (a) go away. Run the program again for five random matrices and comment on the various norms. Do they have a connection with the cond(Aq) (c) Replace then diagonal entries of S by their sixth powers and repeat (b). Do you see significant differences between the results of this exercise and those of the experiment for QR factorization?