Problem 1. Let A = 2 2 2 -5 4 4 -5 (1) Compute the characteristic polynomial of the matrix A. (2) Find the eigenvalue of A and their multiplicities.
Problem 1. Let A = 2 2 2 -5 4 4 -5 (1) Compute the characteristic polynomial of the matrix A. (2) Find the eigenvalue of A and their multiplicities.
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 1.** Let \( A = \begin{pmatrix}
-8 & 2 & 2 \\
2 & -5 & 4 \\
2 & 4 & -5
\end{pmatrix} \).
1. Compute the characteristic polynomial of the matrix \( A \).
2. Find the eigenvalues of \( A \) and their multiplicities.
Define a dynamical system with \( b_0 = \begin{pmatrix}
1 \\
2 \\
3
\end{pmatrix} \) and \( b_{n+1} = A b_n \), for \( n = 1, 2, 3, \ldots \), with \( A \) as in Problem 1. Find a formula for \( b_n \) for each \( n \).
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