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

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Let V and V' be vector spaces over the same field F, and let V be finite dimensional over F. Let dim(V) be the dimension of the vector space V over F. Let ∅ : V → V' be a linear transformation.

a. Show that ∅[VJ is a subspace of V'.

b. Show that dim(∅[V]) = dim(V) - dim(Ker(∅)).

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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 be finite

Question:

Step by Step Answer:

a By group theory we know that V is a subgroup of V Let V and a F Then a a shows that V is closed under multiplication by scalars in F Thus V is a sub...View the full answer

A First Course In Abstract Algebra

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