Let V be the set of all ordered pairs of real numbers, and consider the following addition and scalar multiplication operations on u = (U1, U2) and v = (v1,v2): u + v = (U1 + 01, u2 + v2), ku = (0, kuz) (a) Compute u + v and ku for u =(-1,2), v = (3,4), and k = 3. (b) In words, explain why V is closed under addition and scalar multiplication. (c) Since addition on V is the standard addition operation on R², certain vector space axioms hold for V because they are known to hold for RP. Which axioms are they? (d) Show that Axioms 7, 8, and 9 hold. (e) Show that Axiom 10 fails and hence that V is not a vector space under the given operations.