8 (cid:21)(cid:19). (you may use the following hint: first write (cid:20) 9. 4 (cid:21) and then use properties in the de nition of linear. T (cid:18)(cid:20) 5 as a linear combination of (cid:20) 6 transformation. : (9 points) let a = . 3 1 (a) find a basis for col a. (b) find an orthogonal basis for col a. (c) let w = cola. Find two vectors in w : (9 points) let ~p1(t) = 1 + 4t + t2, ~p2(t) = 1 5t + 4t2, ~p3(t) = 2 + 8t + 2t2 be polynomials in. Explain. (b) let h = span {~p1, ~p2, ~p3}. Find a basis b for h. (c) let ~p(t) = 5+ 2t +11t2 . If so, write the coordinates of ~p with respect to the basis b you found in part (b): (6 points) w = {all diagonal matrices in m2 2 with the diagonal entries integers. }.
