Let A Rnm be a matrix. (a) Show that for each b im(A) there is a unique x0 ker(A) such that Ax0 = b. (b) Show that for each b Rn there is a unique x0 ker(A) such that b Ax0 im(A). (c) Let TA+ : Rn Rm be the function defined for each b Rn as TA+(b) = x0, where x0 ker(A) is the unique vector such that b Ax0 im(A). Show that TA+ is a linear transformation. (d) Show that if ker(A) = {0} and the QR factorization of A is A = QR, then the standard matrix of TA+ defin