Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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## Eigenvalue and Eigenvector Problems ### Problem 1 **Matrix \( \mathbf{A} \):** \[ \mathbf{A} = \begin{bmatrix} -2 & -2 \\ 4 & 7 \end{bmatrix} \] **Given:** - An eigenvalue \( \lambda = 6 \). **Task:** - Find an eigenvector for this eigenvalue. **Eigenvector:** \[ \begin{bmatrix} \text{[Blank]} \\ \text{[Blank]} \end{bmatrix} \] --- ### Problem 2 **Note:** You should solve the following problem **without** computing all eigenvalues. **Matrix \( \mathbf{B} \):** \[ \mathbf{B} = \begin{bmatrix} -4 & -3 \\ -3 & 4 \end{bmatrix} \] **Given:** - An eigenvector \( \mathbf{v} = \begin{bmatrix} -2 \\ 6 \end{bmatrix} \). **Task:** - Find the eigenvalue for this eigenvector. **Eigenvalue:** \[ \lambda = \text{[Blank]} \]
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Transcribed Image Text:## Eigenvalue and Eigenvector Problems ### Problem 1 **Matrix \( \mathbf{A} \):** \[ \mathbf{A} = \begin{bmatrix} -2 & -2 \\ 4 & 7 \end{bmatrix} \] **Given:** - An eigenvalue \( \lambda = 6 \). **Task:** - Find an eigenvector for this eigenvalue. **Eigenvector:** \[ \begin{bmatrix} \text{[Blank]} \\ \text{[Blank]} \end{bmatrix} \] --- ### Problem 2 **Note:** You should solve the following problem **without** computing all eigenvalues. **Matrix \( \mathbf{B} \):** \[ \mathbf{B} = \begin{bmatrix} -4 & -3 \\ -3 & 4 \end{bmatrix} \] **Given:** - An eigenvector \( \mathbf{v} = \begin{bmatrix} -2 \\ 6 \end{bmatrix} \). **Task:** - Find the eigenvalue for this eigenvector. **Eigenvalue:** \[ \lambda = \text{[Blank]} \]
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