Answered: (4) Prove that if A is an eigenvalue of…

(4) Prove that if A is an eigenvalue of an invertible matrix A and x is a corresponding eigenvec- tor, then 1/A is an eigenvalue of A- and x is a corresponding eigenvector.

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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(4) Prove that if A is an eigenvalue of an invertible matrix A and x is a corresponding eigenvec-
tor, then 1/A is an eigenvalue of A¯1 and x is a corresponding eigenvector.

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