Let V and W be vector spaces, and let T :V → W 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.
Let V and W be vector spaces, and let T :V → W 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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 24EQ
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