4. Let V = {p(x) E P2 (R) | p( 2) - 0} and W = W ER' y-2w+ z =0 > be vector spaces. Consider the map T : V -> W defined by(*) T(a(-2- I) + b(4 - 22)) - a, be R. -a -+ 2b [5 marks] (A) Show that T satisfies the additive property of a linear transformation (map). [10 marks] (B) Show that V is isomorphic to W (i.e., V and W are isomorphic). (*) Remark: If you wish: B = {pi(x), p2(x)} = {-2 -z, 4-z'} is a basis for V, and c- fo , is a basis for IV