Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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6. Show all the steps clearly please
6. Let T is a linear operator on a finite-dimensional vector space V. Prove that V R(T) + N(T) implies V R(T) = N(T). Give a counter-example to this statement in the case when V is infinite-dimensional. =
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Transcribed Image Text:6. Let T is a linear operator on a finite-dimensional vector space V. Prove that V R(T) + N(T) implies V R(T) = N(T). Give a counter-example to this statement in the case when V is infinite-dimensional. =
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