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Problem 8. Let V, W be finite dimensional vector spaces over F, and let T € L(V, W) be surjective. Prove that there exists a subspace UCV such that Tu is an isomorphism from U to W. (Here, Tu denotes the restriction of T to U CV.)

Problem 8. Let V, W be finite dimensional vector spaces over F, and let T € L(V, W) be surjective. Prove that there exists a subspace UCV such that Tu is an isomorphism from U to W. (Here, Tu denotes the restriction of T to U CV.)

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...
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Problem 8. Let V, W be finite dimensional vector spaces over F, and let T = L(V, W) be surjective. Prove that there exists a subspace U CV such that Tu is an isomorphism from U to W. (Here, Tu denotes the restriction of T to U CV.)
Transcribed Image Text:Problem 8. Let V, W be finite dimensional vector spaces over F, and let T = L(V, W) be surjective. Prove that there exists a subspace U CV such that Tu is an isomorphism from U to W. (Here, Tu denotes the restriction of T to U CV.)
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