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Exercise 8.9.1 Find the algebraic and geometric multiplicity of each eigenvalue of the following matrices. Which of the matrices are diagonalizable? (c) C = 1 1 (a) A = [4] .]. -1 3 -1 4 2 -1 1 -1 (d) D= (b) B= 3 1 0 2 0 -1 1 4 -7 8 -4 5 (e) E= -2 -1 -2 10 01

Exercise 8.9.1 Find the algebraic and geometric multiplicity of each eigenvalue of the following matrices. Which of the matrices are diagonalizable? (c) C = 1 1 (a) A = [4] .]. -1 3 -1 4 2 -1 1 -1 (d) D= (b) B= 3 1 0 2 0 -1 1 4 -7 8 -4 5 (e) E= -2 -1 -2 10 01

Advanced Engineering Mathematics
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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**Exercise 8.9.1** Find the algebraic and geometric multiplicity of each eigenvalue of the following matrices. Which of the matrices are diagonalizable? (a) \( A = \begin{bmatrix} 1 & 1 \\ -1 & 3 \end{bmatrix} \) (b) \( B = \begin{bmatrix} -7 & 8 \\ -4 & 5 \end{bmatrix} \) (c) \( C = \begin{bmatrix} 2 & -1 & -1 \\ 0 & 4 & 2 \\ 0 & -1 & 1 \end{bmatrix} \) (d) \( D = \begin{bmatrix} 3 & 1 & -1 \\ 0 & 2 & 1 \\ 0 & -1 & 4 \end{bmatrix} \) (e) \( E = \begin{bmatrix} -2 & 0 & 1 \\ -1 & -1 & 1 \\ -2 & 1 & 0 \end{bmatrix} \)
Transcribed Image Text:**Exercise 8.9.1** Find the algebraic and geometric multiplicity of each eigenvalue of the following matrices. Which of the matrices are diagonalizable? (a) \( A = \begin{bmatrix} 1 & 1 \\ -1 & 3 \end{bmatrix} \) (b) \( B = \begin{bmatrix} -7 & 8 \\ -4 & 5 \end{bmatrix} \) (c) \( C = \begin{bmatrix} 2 & -1 & -1 \\ 0 & 4 & 2 \\ 0 & -1 & 1 \end{bmatrix} \) (d) \( D = \begin{bmatrix} 3 & 1 & -1 \\ 0 & 2 & 1 \\ 0 & -1 & 4 \end{bmatrix} \) (e) \( E = \begin{bmatrix} -2 & 0 & 1 \\ -1 & -1 & 1 \\ -2 & 1 & 0 \end{bmatrix} \)
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