Find an eigenvector for this eigenvalue.Note: You should solve the following problem WITHOUT computing all eigenvalues.5 2-3 3 has an eigenvector i3 16The matrix B-523Find the eigenvalue for this eigenvector.= 4 -5 -9The matrix A = 00 -3 has an eigenvalue A = -3.1-2 -3

Answered: 5 2] -5 -3 3 has an eigenvector i 3 1 6…

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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Find an eigenvector for this eigenvalue.
Note: You should solve the following problem WITHOUT computing all eigenvalues.
5 2
-3 3 has an eigenvector i
3 1
6
The matrix B
-5
2
3
Find the eigenvalue for this eigenvector.
=

4 -5 -9
The matrix A = 0
0 -3 has an eigenvalue A = -3.
1
-2 -3

Expert Solution

Step 1

Since you have not mentioned clearly which question to attempt we have answered the first question with matrix B. If you want other question to be answered kindly repost the question and mention the question to be answered.

Given matrix $B = [\begin{matrix} 6 & 5 & 2 \\ - 5 & - 3 & 3 \\ 3 & 3 & 1 \end{matrix}] and eigen vector \vec{v} = [\begin{matrix} - 1 \\ 2 \\ - 1 \end{matrix}]$ .

If $\vec{v}$ is eigen vector of B and $λ$ is the corresponding eigenvalue, we know that

$B \vec{v} = λ \vec{v}$

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