Is v= 3 {} -2 an eigenvector of A = 1 -4 3 2 -3 - 1 3 -2 ? If so, find the eigenvalue. 0 -2 Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Yes, v is an eigenvector of A. The eigenvalue is λ = 0. B. No, v is not an eigenvector of A.
Is v= 3 {} -2 an eigenvector of A = 1 -4 3 2 -3 - 1 3 -2 ? If so, find the eigenvalue. 0 -2 Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Yes, v is an eigenvector of A. The eigenvalue is λ = 0. B. No, v is not an eigenvector of A.
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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Transcribed Image Text:**Problem Statement:**
Determine if the vector \( v = \begin{bmatrix} 3 \\ -2 \\ 1 \end{bmatrix} \) is an eigenvector of the matrix \( A = \begin{bmatrix} -4 & 3 & 3 \\ 2 & -3 & -2 \\ -1 & 0 & -2 \end{bmatrix} \). If it is, find the eigenvalue.
---
**Choices:**
Select the correct choice below and, if necessary, fill in the answer box within your choice.
- **A.** Yes, \( v \) is an eigenvector of \( A \). The eigenvalue is \( \lambda = \, \_\_\_ \).
- **B.** No, \( v \) is not an eigenvector of \( A \).
![**Is \( \lambda = 9 \) an eigenvalue of**
\[
\begin{bmatrix}
8 & 0 & -3 \\
2 & 8 & 5 \\
-3 & 4 & 4
\end{bmatrix}
\]
**? If so, find one corresponding eigenvector.**
---
**Select the correct choice below and, if necessary, fill in the answer box within your choice.**
A. Yes, \( \lambda = 9 \) is an eigenvalue of
\[
\begin{bmatrix}
8 & 0 & -3 \\
2 & 8 & 5 \\
-3 & 4 & 4
\end{bmatrix}
\]
. One corresponding eigenvector is \(\underline{\hspace{1cm}}\).
*(Type a vector or list of vectors. Type an integer or simplified fraction for each matrix element.)*
B. No, \( \lambda = 9 \) is not an eigenvalue of
\[
\begin{bmatrix}
8 & 0 & -3 \\
2 & 8 & 5 \\
-3 & 4 & 4
\end{bmatrix}
\]
.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe00cebfb-aec4-474d-8979-79a2d105b819%2Fe3e49eb1-4c48-4d84-8f5f-eb61b4f8b9a2%2Fa879b6v_processed.png&w=3840&q=75)
Transcribed Image Text:**Is \( \lambda = 9 \) an eigenvalue of**
\[
\begin{bmatrix}
8 & 0 & -3 \\
2 & 8 & 5 \\
-3 & 4 & 4
\end{bmatrix}
\]
**? If so, find one corresponding eigenvector.**
---
**Select the correct choice below and, if necessary, fill in the answer box within your choice.**
A. Yes, \( \lambda = 9 \) is an eigenvalue of
\[
\begin{bmatrix}
8 & 0 & -3 \\
2 & 8 & 5 \\
-3 & 4 & 4
\end{bmatrix}
\]
. One corresponding eigenvector is \(\underline{\hspace{1cm}}\).
*(Type a vector or list of vectors. Type an integer or simplified fraction for each matrix element.)*
B. No, \( \lambda = 9 \) is not an eigenvalue of
\[
\begin{bmatrix}
8 & 0 & -3 \\
2 & 8 & 5 \\
-3 & 4 & 4
\end{bmatrix}
\]
.
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