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3) Suppose T E L(V) and T² = I and -1 is not an eigenvalue of T. Prove that T = 1. %3D

3) Suppose T E L(V) and T² = I and -1 is not an eigenvalue of T. Prove that T = 1. %3D

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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Prove that 1 = 2 or a = 3 or 1 = 4. Assume the field of scalars is C, R, or Q. 3) Suppose T E L(V) and T² = I and –1 is not an eigenvalue of T. Prove that T = 1. 4) Give an example of an operator whose matrix with respect to some basis contains only O's on the diagonal, but the operator is invertible, or explain why there can be no such
Transcribed Image Text:Prove that 1 = 2 or a = 3 or 1 = 4. Assume the field of scalars is C, R, or Q. 3) Suppose T E L(V) and T² = I and –1 is not an eigenvalue of T. Prove that T = 1. 4) Give an example of an operator whose matrix with respect to some basis contains only O's on the diagonal, but the operator is invertible, or explain why there can be no such
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