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If T : V → W and U : W → Z are linear transformations, prove that rank(UT) < rank(T). (Hint: How does N(UT) compare with N(T)?]

If T : V → W and U : W → Z are linear transformations, prove that rank(UT) < rank(T). (Hint: How does N(UT) compare with N(T)?]

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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If T :V → W and U : W → Z are linear transformations, prove that rank(UT) < rank(T). (Hint: How does N(UT) compare with N(T)?]
Transcribed Image Text:If T :V → W and U : W → Z are linear transformations, prove that rank(UT) < rank(T). (Hint: How does N(UT) compare with N(T)?]
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