(a) Prove that a homomorphism is onto if and only if its rank equals the dimension of...

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(a) Prove that a homomorphism is onto if and only if its rank equals the dimension of its codomain.
(b) Conclude that a homomorphism between vector spaces with the same dimension is one-to-one if and only if it is onto.

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Linear Algebra

ISBN: 9780982406212

1st Edition

Authors: Jim Hefferon

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Question Posted: Jun 01, 2016 02:01 AM

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(a) Prove that a homomorphism is onto if and only if its rank equals the dimension of...

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a One direction is obvious if the homomorphism is onto then its range is the codomain and so its ran...View the full answer

Linear Algebra

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