Suppose A has eigenvalue X = - 1 with corresponding eigenvector u = [1]. 4 with corresponding eigenvector Find the following. A¹⁰u = [8] = 3 A¹0= (8) and eigenvalue X = 2
Suppose A has eigenvalue X = - 1 with corresponding eigenvector u = [1]. 4 with corresponding eigenvector Find the following. A¹⁰u = [8] = 3 A¹0= (8) and eigenvalue X = 2
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 \( A \) has eigenvalue \( \lambda = -1 \) with corresponding eigenvector \( \vec{u} = \begin{bmatrix} 1 \\ 4 \end{bmatrix} \), and eigenvalue \( \lambda = 2 \) with corresponding eigenvector \( \vec{v} = \begin{bmatrix} 1 \\ 3 \end{bmatrix} \).
Find the following:
\[
A^{10} \vec{u} = \begin{bmatrix} \Box \\ \Box \end{bmatrix}, \quad A^{10} \vec{v} = \begin{bmatrix} \Box \\ \Box \end{bmatrix}
\]
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Transcribed Image Text:Suppose \( A \) has eigenvalue \( \lambda = -1 \) with corresponding eigenvector \( \vec{u} = \begin{bmatrix} 1 \\ 4 \end{bmatrix} \), and eigenvalue \( \lambda = 2 \) with corresponding eigenvector \( \vec{v} = \begin{bmatrix} 1 \\ 3 \end{bmatrix} \).
Find the following:
\[
A^{10} \vec{u} = \begin{bmatrix} \Box \\ \Box \end{bmatrix}, \quad A^{10} \vec{v} = \begin{bmatrix} \Box \\ \Box \end{bmatrix}
\]
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