Crixn. Find a basis for sI(n, C). What is the dimension of sl(n, C)? P16.3. Let T : V - W be a linear map. (i) Let v1, V2,..., Un be linearly independent vectors in the K-vector space V. When T is injective, prove that the vectors T[vi], T [v2], ..., T[Un] are linearly independent in the K-vector space W. (ii) Consider vectors v1, v2, ..., , that span the K-vector space V. When the map T is surjective, prove that the vectors T[vi], T [v2], ..., T [v,] span the K-vector space W. (iii) Let v1, V2,..., Un be a basis for the K-vector space V. When the map 7 is bijective, prove that the vectors T[vi], T [v2], ..., T [Un] are basis for the K-vector space W