Q1) . Let V be the set of all ordered pairs of real numbers, and consider the following addition and scalar multiplication op- erations on u = (u1, u2) and v = (v1, v2): u+v = (u, + Vj + 1, u2 + vz +...

Extracted text: Q1) . Let V be the set of all ordered pairs of real numbers, and consider the following addition and scalar multiplication op- erations on u = (u1, u2) and v = (v1, v2): u+v = (u, + Vj + 1, u2 + vz + 1), ku = (ku1, ku2) (a) Compute u +v and ku for u = (0, 4), v = (1, –3), and k = 2. (b) Show that (0, 0) # 0. (c) Show that (-1, –1) = 0. (d) Show that Axiom 5 holds by producing an ordered pair -u such that u + (-u) = 0 for u = (u1, u2). (e) Find two vector space axioms that fail to hold.