:) the the following matrices diagnalizable? If yes, determine their diagonal form and a basis with respect to which the nsformation matrices are diagonal. If no, give reasons why they not ·licable
:) the the following matrices diagnalizable? If yes, determine their diagonal form and a basis with respect to which the nsformation matrices are diagonal. If no, give reasons why they not ·licable
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
4.7
![**4.7** Are the following matrices diagonalizable? If yes, determine their diagonal form and a basis with respect to which the transformation matrices are diagonal. If no, give reasons why they are not diagonalizable.
a)
\[ A = \begin{bmatrix} 0 & 1 \\ -8 & 4 \end{bmatrix} \]
b)
\[ \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix} \]
c)
\[ \begin{bmatrix} 5 & 4 & 2 & 1 \\ 0 & 7 & -1 & 1 \\ -1 & 3 & 3 & 0 \\ 1 & 1 & 1 & 2 \end{bmatrix} \]
d)
\[ A = \begin{bmatrix} 5 & -6 & -6 \\ -1 & 4 & 2 \\ 3 & -6 & -4 \end{bmatrix} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e25041d-7573-46df-b9d3-ec2dd7694c16%2F2adcd7ab-5c45-49d6-b8af-9a0cf6f8f945%2Fu60er7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**4.7** Are the following matrices diagonalizable? If yes, determine their diagonal form and a basis with respect to which the transformation matrices are diagonal. If no, give reasons why they are not diagonalizable.
a)
\[ A = \begin{bmatrix} 0 & 1 \\ -8 & 4 \end{bmatrix} \]
b)
\[ \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix} \]
c)
\[ \begin{bmatrix} 5 & 4 & 2 & 1 \\ 0 & 7 & -1 & 1 \\ -1 & 3 & 3 & 0 \\ 1 & 1 & 1 & 2 \end{bmatrix} \]
d)
\[ A = \begin{bmatrix} 5 & -6 & -6 \\ -1 & 4 & 2 \\ 3 & -6 & -4 \end{bmatrix} \]
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