Prove that the image of a span equals the span of the images. That is, where h:

Question:

Prove that the image of a span equals the span of the images. That is, where h: V → W is linear, prove that if S is a subset of V then h([S]) equals [h(S)]. This generalizes Lemma 2.1 since it shows that if U is any subspace of V then its image {h() | ∈ U} is a subspace of W, because the span of the set U is U.