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Suppose A is a matrix with eigenvalues A1 = 1, A, = 2, A3 = -3, with corresponding eigenvectors v1 =, V2 =, -1 V3 = | 2 [12 , find A17x. respectively. Given the vector x = -1 3

Suppose A is a matrix with eigenvalues A1 = 1, A, = 2, A3 = -3, with corresponding eigenvectors v1 =, V2 =, -1 V3 = | 2 [12 , find A17x. respectively. Given the vector x = -1 3

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 a matrix with eigenvalues \( \lambda_1 = 1 \), \( \lambda_2 = 2 \), \( \lambda_3 = -3 \), with corresponding eigenvectors \( \mathbf{v}_1 = \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} \), \( \mathbf{v}_2 = \begin{bmatrix} 2 \\ -1 \\ 1 \end{bmatrix} \), and \( \mathbf{v}_3 = \begin{bmatrix} 1 \\ 2 \\ 1 \end{bmatrix} \) respectively. Given the vector \( \mathbf{x} = \begin{bmatrix} 12 \\ -1 \\ 3 \end{bmatrix} \), find \( A^{17} \mathbf{x} \).
Transcribed Image Text:Suppose \( A \) is a matrix with eigenvalues \( \lambda_1 = 1 \), \( \lambda_2 = 2 \), \( \lambda_3 = -3 \), with corresponding eigenvectors \( \mathbf{v}_1 = \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} \), \( \mathbf{v}_2 = \begin{bmatrix} 2 \\ -1 \\ 1 \end{bmatrix} \), and \( \mathbf{v}_3 = \begin{bmatrix} 1 \\ 2 \\ 1 \end{bmatrix} \) respectively. Given the vector \( \mathbf{x} = \begin{bmatrix} 12 \\ -1 \\ 3 \end{bmatrix} \), find \( A^{17} \mathbf{x} \).
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