Question
Asked Jul 17, 2019

Differential equations

Find the general solution to the given systems of equations. Please refer to attached image.

T
= X
T
X
- 2
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T = X T X - 2

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Step 1

Hey, since there are multiple subparts posted, we will answer first question. If you want any specific question to be answered then please submit that question only or specify the question number in your message

a)

Obtain the Eigen values for the matrix as follows.

The eigenvalues of Aaretheroots of the characteristicequation det (A -2I)0
-3
det
1
- 2
-2
0
=0
1
-3 - 2
= 0
/2
-2 -A
524= 0
(2+1)(2+4) 0
1-4
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The eigenvalues of Aaretheroots of the characteristicequation det (A -2I)0 -3 det 1 - 2 -2 0 =0 1 -3 - 2 = 0 /2 -2 -A 524= 0 (2+1)(2+4) 0 1-4

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Step 2

Obtain the eigenvectors for eigenvalue is –1 as follows.

Eigenvectors for 2 = -1
-3 2
1 0
-(-)
0 1
A-AI
2
-2 2
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Eigenvectors for 2 = -1 -3 2 1 0 -(-) 0 1 A-AI 2 -2 2

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Step 3

The reduce matrix to reduced row echel...

-2 V2
|R,R
0
-2 /2
0
-1
2R
2
0
0
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-2 V2 |R,R 0 -2 /2 0 -1 2R 2 0 0

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