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Supppose A is an invertible n x n matrix and v is an eigenvector of A with associated eigenvalue -6. Convince yourself that v is an eigenvector of the following matrices, and find the associated eigenvalues: 1. A?, eigenvalue = 2. A-1, eigenvalue = 3. A+ 5In, eigenvalue =

Supppose A is an invertible n x n matrix and v is an eigenvector of A with associated eigenvalue -6. Convince yourself that v is an eigenvector of the following matrices, and find the associated eigenvalues: 1. A?, eigenvalue = 2. A-1, eigenvalue = 3. A+ 5In, eigenvalue =

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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Suppose \( A \) is an invertible \( n \times n \) matrix and \( \mathbf{v} \) is an eigenvector of \( A \) with associated eigenvalue \(-6\). Convince yourself that \( \mathbf{v} \) is an eigenvector of the following matrices, and find the associated eigenvalues: 1. \( A^2 \), eigenvalue = \(\_\_\_\_\) 2. \( A^{-1} \), eigenvalue = \(\_\_\_\_\) 3. \( A + 5I_n \), eigenvalue = \(\_\_\_\_\) 4. \( 4A \), eigenvalue = \(\_\_\_\_\)
Transcribed Image Text:Suppose \( A \) is an invertible \( n \times n \) matrix and \( \mathbf{v} \) is an eigenvector of \( A \) with associated eigenvalue \(-6\). Convince yourself that \( \mathbf{v} \) is an eigenvector of the following matrices, and find the associated eigenvalues: 1. \( A^2 \), eigenvalue = \(\_\_\_\_\) 2. \( A^{-1} \), eigenvalue = \(\_\_\_\_\) 3. \( A + 5I_n \), eigenvalue = \(\_\_\_\_\) 4. \( 4A \), eigenvalue = \(\_\_\_\_\)
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