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Find all distinct eigenvalues of A. Then find the basic eigenvectors of A corresponding to each eigenvalue. For each eigenvalue, specify the number of basic eigenvectors corresponding to that eigenvalue, then enter the eigenvalue followed by the basic eigenvectors corresponding to that eigenvalue. [-3 2 6 A = 0 1 6 0-1 -4 Number of distinct eigenvalues: 1 Number of Vectors: 1

Find all distinct eigenvalues of A. Then find the basic eigenvectors of A corresponding to each eigenvalue. For each eigenvalue, specify the number of basic eigenvectors corresponding to that eigenvalue, then enter the eigenvalue followed by the basic eigenvectors corresponding to that eigenvalue. [-3 2 6 A = 0 1 6 0-1 -4 Number of distinct eigenvalues: 1 Number of Vectors: 1

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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Find all distinct eigenvalues of \( A \). Then find the basic eigenvectors of \( A \) corresponding to each eigenvalue. For each eigenvalue, specify the number of basic eigenvectors corresponding to that eigenvalue, then enter the eigenvalue followed by the basic eigenvectors corresponding to that eigenvalue. \[ A = \begin{bmatrix} -3 & 2 & 6 \\ 0 & 1 & 6 \\ 0 & -1 & -4 \end{bmatrix} \] Number of distinct eigenvalues: \(\underline{1}\) Number of Vectors: \(\underline{1}\) \[ 0: \left\lbrace \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix} \right\rbrace \]
Transcribed Image Text:Find all distinct eigenvalues of \( A \). Then find the basic eigenvectors of \( A \) corresponding to each eigenvalue. For each eigenvalue, specify the number of basic eigenvectors corresponding to that eigenvalue, then enter the eigenvalue followed by the basic eigenvectors corresponding to that eigenvalue. \[ A = \begin{bmatrix} -3 & 2 & 6 \\ 0 & 1 & 6 \\ 0 & -1 & -4 \end{bmatrix} \] Number of distinct eigenvalues: \(\underline{1}\) Number of Vectors: \(\underline{1}\) \[ 0: \left\lbrace \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix} \right\rbrace \]
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