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and W be vector spaces and A : V → W be a linear map. (b) Let V, W be a pair of vector spaces and A : V → W be a linear one image. Then A(V ) is a linear subspace of W. Prove that A(V )= Im(A), the image of A, is a linear subspace of W.

and W be vector spaces and A : V → W be a linear map. (b) Let V, W be a pair of vector spaces and A : V → W be a linear one image. Then A(V ) is a linear subspace of W. Prove that A(V )= Im(A), the image of A, is a linear subspace of W.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.CR: Review Exercises
Problem 78CR: Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set...
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Let V and W be vector spaces and A : V → W be a linear map.

(b) Let V, W be a pair of vector spaces and A : V → W be a linear one
image. Then A(V ) is a linear subspace of W. Prove that A(V )= Im(A), the image of A, is a linear subspace
of W.

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