Let λ be an eigenvalue of invertible matrix A. Prove that exists and is an eigenvalue of A-¹. What does your proof also say about the corresponding eigenvector?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.5: Eigenvalues And Eigenvectors
Problem 14E: In exercise 14 and 15, each 22matrix has only one eigenvalue. Find the eigenvalue and the...
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Let A be an eigenvalue of invertible matrix A. Prove that
exists
and is an eigenvalue of A-¹. What does your proof also say about
the corresponding eigenvector?
Transcribed Image Text:Let A be an eigenvalue of invertible matrix A. Prove that exists and is an eigenvalue of A-¹. What does your proof also say about the corresponding eigenvector?
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