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 + v1 + 1, u2 + v2 + 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)