a) (5 points) Let V and W be vector spaces over R, and let T : V - W be a linear map. Let {v1, 02,."., Un} be vectors in V such that {T(1), T(12),..., T(Un)} is a linearly independent set in W. Prove that {01, 02,.", Un} is linearly independent. b) (5 points) Let V be a vector space over R, and let T : V - It be a linear map. Suppose 71, 02, 03, 04 E V are such that T(v1) = (1,0,0,0), T(3,) = (1, 1,0,0), T(73) = (1, 1, 1,0), T(74) = (1,1,1,1). Prove that dim(V) 2 4