Exercise 8.11.1 Find the (real or complex) eigenvalues and eigenvectors of the following matrices. Diag- onalize each matrix if possible. A = 1 [42] - 1 -2 -[13]. B = C= 2 -1 3 0 1 1 1 0 D = 1 1 -1 1 20
Exercise 8.11.1 Find the (real or complex) eigenvalues and eigenvectors of the following matrices. Diag- onalize each matrix if possible. A = 1 [42] - 1 -2 -[13]. B = C= 2 -1 3 0 1 1 1 0 D = 1 1 -1 1 20
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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Can you please solve the problem A & B ?
![**Exercise 8.11.1** Find the (real or complex) eigenvalues and eigenvectors of the following matrices. Diagonalize each matrix if possible.
\[
A = \begin{bmatrix} 2 & 1 \\ -1 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} -1 & -2 \\ 1 & 1 \end{bmatrix}
\]
\[
C = \begin{bmatrix} 2 & -1 & 3 \\ 0 & 1 & 1 \\ -1 & 1 & 0 \end{bmatrix}, \quad D = \begin{bmatrix} 1 & 1 & 1 \\ -1 & 2 & 0 \\ 1 & -1 & 1 \end{bmatrix}
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Transcribed Image Text:**Exercise 8.11.1** Find the (real or complex) eigenvalues and eigenvectors of the following matrices. Diagonalize each matrix if possible.
\[
A = \begin{bmatrix} 2 & 1 \\ -1 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} -1 & -2 \\ 1 & 1 \end{bmatrix}
\]
\[
C = \begin{bmatrix} 2 & -1 & 3 \\ 0 & 1 & 1 \\ -1 & 1 & 0 \end{bmatrix}, \quad D = \begin{bmatrix} 1 & 1 & 1 \\ -1 & 2 & 0 \\ 1 & -1 & 1 \end{bmatrix}
\]
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