Problem 3 Let Le Rnxn be a symmetric positive semidefinite matrix with ker(L) = span{1}. Let also P = [p1|p2| ... |Pn-1] Rnx(n-1) be a projection matrix on 1+, so that p Pj = 0, p 1 = 0, and ||pi|| = 1 for all column vectors i, j of P. Show that (a) if 11(L) \2(L) ||2||2. Problem 3 Let Le Rnxn be a symmetric positive semidefinite matrix with ker(L) = span{1}. Let also P = [p1|p2| ... |Pn-1] Rnx(n-1) be a projection matrix on 1+, so that p Pj = 0, p 1 = 0, and ||pi|| = 1 for all column vectors i, j of P. Show that (a) if 11(L) \2(L) ||2||2