Let V and W be finite - dimensional vector spaces and let T : V rightarrow W be linear as well as one - to - one and onto. Suppose that dim(V) = n and let beta = {vi,... vn} be a basis for V. Prove that {T(v1),..., T(vn)} is a basis for W. Let U : W rightarrow V be the unique linear map such that U(T(vi)) = Vi for all 1
