2 Suppose that A = 2 1 Find the eigenvectors of A 1 0 -1
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 that
\[
A = \begin{pmatrix} 2 & 0 & 0 \\ -2 & 1 & 0 \\ 1 & 0 & -1 \end{pmatrix}
\]
Find the eigenvectors of \( A \).
(a) Eigenvector with respect to the smallest eigenvalue: \( \vec{v}_1 = \)
\[
\begin{bmatrix}
\boxed{} \\
\boxed{} \\
\boxed{}
\end{bmatrix}
\]
where \( \vec{v}_1 \) is a unit vector;
(b) Eigenvector with respect to the second smallest eigenvalue: \( \vec{v}_2 = \)
\[
\begin{bmatrix}
\boxed{} \\
\boxed{} \\
\boxed{}
\end{bmatrix}
\]
where \( \vec{v}_2 \) is a unit vector;
(c) Eigenvector with respect to the biggest eigenvalue: \( \vec{v}_3 = \)
\[
\begin{bmatrix}
\boxed{} \\
\boxed{} \\
\boxed{}
\end{bmatrix}
\]
where \( \vec{v}_3 \) is a unit vector.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2a435ab-e32d-4bb5-91c7-35592295b90b%2F33eb83ca-d43a-4c9a-b23b-c1d0e0f0d4bb%2Fd1rzm4_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that
\[
A = \begin{pmatrix} 2 & 0 & 0 \\ -2 & 1 & 0 \\ 1 & 0 & -1 \end{pmatrix}
\]
Find the eigenvectors of \( A \).
(a) Eigenvector with respect to the smallest eigenvalue: \( \vec{v}_1 = \)
\[
\begin{bmatrix}
\boxed{} \\
\boxed{} \\
\boxed{}
\end{bmatrix}
\]
where \( \vec{v}_1 \) is a unit vector;
(b) Eigenvector with respect to the second smallest eigenvalue: \( \vec{v}_2 = \)
\[
\begin{bmatrix}
\boxed{} \\
\boxed{} \\
\boxed{}
\end{bmatrix}
\]
where \( \vec{v}_2 \) is a unit vector;
(c) Eigenvector with respect to the biggest eigenvalue: \( \vec{v}_3 = \)
\[
\begin{bmatrix}
\boxed{} \\
\boxed{} \\
\boxed{}
\end{bmatrix}
\]
where \( \vec{v}_3 \) is a unit vector.
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