Please answer number 5. **Problem 4**Determine whether the following matrices are diagonalizable or not. Explain your answer.1. $ A = \begin{bmatrix} 1 & 5 \\ 0 & 2 \end{bmatrix} $.2. $ B = \begin{bmatrix} 2 & 2 \\ 0 & 2 \end{bmatrix} $.3. $ C = \begin{bmatrix} 2 & 2 \\ 2 & 2 \end{bmatrix} $.4. $ D = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix} $.5. $ E = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix} $.

Answered: 0 0 0 1 1 0 1 E =

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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Question

Please answer number 5.

**Problem 4**

Determine whether the following matrices are diagonalizable or not. Explain your answer.

1. $ A = \begin{bmatrix} 1 & 5 \\ 0 & 2 \end{bmatrix} $.

2. $ B = \begin{bmatrix} 2 & 2 \\ 0 & 2 \end{bmatrix} $.

3. $ C = \begin{bmatrix} 2 & 2 \\ 2 & 2 \end{bmatrix} $.

4. $ D = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix} $.

5. $ E = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix} $.

Expert Solution

Step 1

as you asking for only queston number 5, i solve for you that

Here E

0	0	1
0	1	0
1	0	0

Find eigenvalues of the matrix A

|E-λI|=0

(-λ)	0	1
0	(1-λ)	0
1	0	(-λ)

= 0

∴(-λ)((1-λ)×(-λ)-0×0)-0(0×(-λ)-0×1)+1(0×0-(1-λ)×1)=0

∴(-λ)((-λ+λ2)-0)-0(0-0)+1(0-(1-λ))=0

∴(-λ)(-λ+λ2)-0(0)+1(-1+λ)=0

∴(λ2-λ3)-0+(-1+λ)=0

∴(-λ3+λ2+λ-1)=0

∴-(λ-1)(λ-1)(λ+1)=0

∴(λ-1)=0or(λ-1)=0or(λ+1)=0

∴ The eigenvalues of the matrix E are given by λ=-1,1,

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