Answer: Exercises 31 and 32 concern finite-dimensional
Chapter 4, Problem 31E(choose chapter or problem)
Exercises 31 and 32 concern finite-dimensional vector spaces V and W and a linear transformationT : V Let H be a nonzero subspace of V, and let T (H) be the set of images of vectors in H. Then T (H) is a subspace of W , by Exercise 35 in Section 4.2. Prove that dim T (H) dim HReference:Let V and W be vector spaces, and let T : V be a linear transformation. Given a subspace U of V, let T (U) denote the set of all images of the form T (x), where x is in U. Show that T (U) is a subspace of W.
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