Let V and V' be vector spaces over the same field F, and let : V

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Let V and V' be vector spaces over the same field F, and let ∅ : V → V' be a linear transformation.

a. To what concept that we have studied for the algebraic structures of groups and rings does the concept of a linear transformation correspond?

b. Define the kernel (or nullspace) of ∅, and show that it is a subspace of V.

c. Describe when ∅ is an isomorphism of V with V'.

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A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

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Question Posted: Jan 09, 2023 01:44 AM

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Let V and V' be vector spaces over the same field F, and let : V

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a A linear transformation of vector spaces is analogous to a homomorphism of groups b The ...View the full answer

A First Course In Abstract Algebra

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