Part 3: Proofs/Counterexamples and Computation (3 problems will be graded ran- domly, 3 pts. Ea.) 8. Prove that every vector space has a unique zero vector. 9. Prove that for every vector v in a vector space V, there is a unique v' in V such that v + v' = 0. 10. Let # = {v1, v2, ...,Vn} be a basis for a vector space V. Let u and v be vectors in V and let c be a scalar. Then (a) [utvle = [ul + [vis. (b) cluj = clv]. 11. Let A= ] ] . -{6 )] . 6 )] . 6 9] . 6 ])