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Supppose A is an invertible n x n matrix and v is an eigenvector of A with associated eigenvalue 8. Convince yourself that is an eigenvector of the following matrices, and find the associated eigenvalues. a. The matrix A1 has an eigenvalue ☐. b. The matrix A-1 has an eigenvalue ☐. c. The matrix A + 81 has an eigenvalue ☐. d. The matrix 2A has an eigenvalue ☐.

Supppose A is an invertible n x n matrix and v is an eigenvector of A with associated eigenvalue 8. Convince yourself that is an eigenvector of the following matrices, and find the associated eigenvalues. a. The matrix A1 has an eigenvalue ☐. b. The matrix A-1 has an eigenvalue ☐. c. The matrix A + 81 has an eigenvalue ☐. d. The matrix 2A has an eigenvalue ☐.

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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN: 9781285463247

Author: David Poole

Publisher: Cengage Learning

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Transcribed Image Text:Supppose A is an invertible n x n matrix and v is an eigenvector of A with associated eigenvalue 8. Convince yourself that is an eigenvector of the following matrices, and find the associated eigenvalues. a. The matrix A1 has an eigenvalue ☐. b. The matrix A-1 has an eigenvalue ☐. c. The matrix A + 81 has an eigenvalue ☐. d. The matrix 2A has an eigenvalue ☐.

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