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*Problem 3.15 Prove that Tr(T/T₂) Tr(T₂T₁). It follows immediately that Tr T₁ T₂T₁) Tr(T₂T3T₁), but is it the case that Tr(T, T₂T3) = Tr(T₂T, T₁), in gen- eral? Prove it, or disprove it. Hint: The best disproof is always a counterexample- and the simpler the better!

*Problem 3.15 Prove that Tr(T/T₂) Tr(T₂T₁). It follows immediately that Tr T₁ T₂T₁) Tr(T₂T3T₁), but is it the case that Tr(T, T₂T3) = Tr(T₂T, T₁), in gen- eral? Prove it, or disprove it. Hint: The best disproof is always a counterexample- and the simpler the better!

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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*Problem 3.15 Prove that Tr(T, T₂) Tr(T₂T₁). It follows immediately that TrT, T₂T₁) Tr(T₂T3T₁), but is it the case that Tr(T/T₂T3) = Tr(T₂T, T₁), in gen- eral? Prove it, or disprove it. Hint: The best disproof is always a counterexample- and the simpler the better!
Transcribed Image Text:*Problem 3.15 Prove that Tr(T, T₂) Tr(T₂T₁). It follows immediately that TrT, T₂T₁) Tr(T₂T3T₁), but is it the case that Tr(T/T₂T3) = Tr(T₂T, T₁), in gen- eral? Prove it, or disprove it. Hint: The best disproof is always a counterexample- and the simpler the better!
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