Suppose T E L(V). Prove that the quotient operator T/range T € L(V/range T) is the zero operator. In this case the quotient operator T/range T is defined by (T/range T)(v + range T) = Tv + range T.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.1: The Geometry And Algebra Of Vectors
Problem 24EQ
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6) Suppose T E L(V). Prove that the quotient operator T/range T E L(V/range T) is the
zero operator. In this case the quotient operator T/range T is defined by
(T/range T)(v + range T) = Tv + range T.
Transcribed Image Text:6) Suppose T E L(V). Prove that the quotient operator T/range T E L(V/range T) is the zero operator. In this case the quotient operator T/range T is defined by (T/range T)(v + range T) = Tv + range T.
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