2. The idea of this exercise is to carry out an experiment analogous to the one described in Lec. 16 of the text, but for the SVD instead of QR factorization. (a) Write a program that constructs a 50 x 50 matrix A - U*S*V', where U and V are random orthogonal matrices and S is a diagonal matrix whose diagonal entries are uniformly distributed numbers in [0, 1], sorted into nonincreasing order. You can use the following lines in MATLAB [U , X] = qr (randn (50)); [v , x] = qr (randn (50)); S diag (sort (rand (50,1), 'descend')); Compute the SVD of A: [U2,S2,V2] -svd(A); Recall that the SVD of a real square matrix is not quite uniquely determined. Make sure that the signs of the columns of U2 and V2 match those of U and V as follows: for j-1:50, if U2(: ,j),*U(: ,j)