Let T : V → W be a linear transformation from vector space V to vector space W, both of which are finite-dimensional. Let H be a nonzero subspace of V , and let T(H) = {T(x)| x ∈ H} (i. e., T(H) is the set of images of the vectors in V ). Prove that T(H) is a subspace of W. Also show that dim(T(H)) ≤ dim(H). Recall that dim(H) denotes the dimension of the vector space H.