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-3 and v2 5 If i1 are eigenvectors of a matrix A corresponding to the eigenvalues A1 1 -4 and A2 =-2, respectively, then A(v1 + v2)

-3 and v2 5 If i1 are eigenvectors of a matrix A corresponding to the eigenvalues A1 1 -4 and A2 =-2, respectively, then A(v1 + v2)

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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If \( \vec{v}_1 = \begin{bmatrix} -3 \\ 5 \end{bmatrix} \) and \( \vec{v}_2 = \begin{bmatrix} -4 \\ 1 \end{bmatrix} \) are eigenvectors of a matrix \( A \) corresponding to the eigenvalues \( \lambda_1 = -4 \) and \( \lambda_2 = -2 \), respectively, then \( A(\vec{v}_1 + \vec{v}_2) = \begin{bmatrix} \phantom{0} \\ \phantom{0} \end{bmatrix} \)
Transcribed Image Text:If \( \vec{v}_1 = \begin{bmatrix} -3 \\ 5 \end{bmatrix} \) and \( \vec{v}_2 = \begin{bmatrix} -4 \\ 1 \end{bmatrix} \) are eigenvectors of a matrix \( A \) corresponding to the eigenvalues \( \lambda_1 = -4 \) and \( \lambda_2 = -2 \), respectively, then \( A(\vec{v}_1 + \vec{v}_2) = \begin{bmatrix} \phantom{0} \\ \phantom{0} \end{bmatrix} \)
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