'(16) Consider the map T : P2(F) ?P2(F) de?ned by T(p(x)) =xp'(x).
(a) Prove that T is linear.
(b) What is null(T)?
(c) Compute the matrix M(T) with respect to the bases B and B'of P2(F), where
B = {1,1 + x,1 + x + x2}, B' = {2?x,x + x2,x2}.
(d) Use the matrix M(T) to write T(7x2 + 12x?1) as a linearcombination of the polynomials in the basis B'.
