Let R and S be commutative rings, and o: R S a ring homo- morphism. Let : R[X] S[X] be given by a) Show that b) Show that c) Show that n Caixi i=0 = 2 (). i=0 is a ring homomorphism. is injective if and only if is injective. is surjective if and only if y is surjective. Problem 3. Let V be a vector space over a field k, let WC V be any subset, and let kW = {aw + aw+...+an Wn | ai e k, w W}. Show that kW is a subspace of V.