Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

Find the eigenvalues and corresponding eigenvector spaces for the following matrices

The text presents a matrix and its associated eigenvalues and eigenvectors. Matrix \( C \): \[ C = \begin{bmatrix} 5 & -6 & -6 \\ -1 & 4 & 2 \\ 3 & -6 & -4 \end{bmatrix} \] The eigenvalues and their corresponding eigenvectors are given as follows: - For eigenvalue \(\lambda = 1\), the corresponding eigenvector is \( t(3, -1, 3) \). - For eigenvalue \(\lambda = 2\), the corresponding eigenvector is \( t(2, 2, -1) \). Here, \( t \) is a scalar, indicating that the eigenvectors can be multiplied by any scalar to obtain a valid eigenvector.
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Transcribed Image Text:The text presents a matrix and its associated eigenvalues and eigenvectors. Matrix \( C \): \[ C = \begin{bmatrix} 5 & -6 & -6 \\ -1 & 4 & 2 \\ 3 & -6 & -4 \end{bmatrix} \] The eigenvalues and their corresponding eigenvectors are given as follows: - For eigenvalue \(\lambda = 1\), the corresponding eigenvector is \( t(3, -1, 3) \). - For eigenvalue \(\lambda = 2\), the corresponding eigenvector is \( t(2, 2, -1) \). Here, \( t \) is a scalar, indicating that the eigenvectors can be multiplied by any scalar to obtain a valid eigenvector.
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