Let T1, T2 : V → V be linear transformations satisfying Tị • T2 = ly (where 1y denotes the identity linear transformation from V to itself). Show that T2 • T1 = ly when V is finite-dimensional, but that this need not be the case in general when V is infinite dimensional.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 4EQ
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Let T1, T2 : V → V be linear transformations satisfying Tị • T2 = ly (where 1y denotes the identity
linear transformation from V to itself). Show that T2 • T1 = ly when V is finite-dimensional, but that
this need not be the case in general when V is infinite dimensional.
Transcribed Image Text:Let T1, T2 : V → V be linear transformations satisfying Tị • T2 = ly (where 1y denotes the identity linear transformation from V to itself). Show that T2 • T1 = ly when V is finite-dimensional, but that this need not be the case in general when V is infinite dimensional.
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