For each of the following linear operators T, determine if the given subspace W is a T-invariant subspace of V. (a) V=P3(R), T(f) = f', and W = P2 (R) (b) V=P(R), T(f(x)) = xf(x), and W = P2(R) (c) V=R^3, T(a, b, c) = (a +b+c, a +b+c, a +b+c), and W = {(t,t,t): t ∈ R} (d) V = C([0,1]), T(F(t)) = [∫1 0 f(x) dx)t, and W = {f ∈ V: f(t) = at + b for some a and b} (e) V = M_2x2 (R), T(A) = A= (0 1 1 0)A and V = {A ∈ V: A^t = A}