2. (15pt) Let A be an m-by-n matrix, m > n. Assume that A has full rank. Let . be the solution of the problem of minimizing ||Ac - 6/12, where be R". Consider the singular value de composition of A = UEVT Show that the residual r = A. - bis orthogonal to the columns of U, that is UT, = 0. Recall that columns of U span the range of the linear transformation defined by A. What does the above result means in terms of the range of linear transformation A:R" R"? 2. (15pt) Let A be an m-by-n matrix, m > n. Assume that A has full rank. Let . be the solution of the problem of minimizing ||Ac - 6/12, where be R". Consider the singular value de composition of A = UEVT Show that the residual r = A. - bis orthogonal to the columns of U, that is UT, = 0. Recall that columns of U span the range of the linear transformation defined by A. What does the above result means in terms of the range of linear transformation A:R" R