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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

Section4.3: Subspaces Of Vector Spaces

Problem 52E

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Suppose V is a vector space and T: V → V is a linear operator. A subspace U CV is said
to be T-ambivalent if T(U) CU.
Show that ker(T) and im(T) are T-ambivalent.

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