Question
Asked Oct 22, 2019
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Linear algebra

(7) Solve the following initial value problem,
1
4
-1
di
-1 , o
3
2
3
dt
2
1
-1
You are given that the following vectors are eigenvectors of the matrix A above.
1
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(7) Solve the following initial value problem, 1 4 -1 di -1 , o 3 2 3 dt 2 1 -1 You are given that the following vectors are eigenvectors of the matrix A above. 1

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Expert Answer

Step 1

It is given that,

1 -1 4
3 2-1x. x0
1
d x
3
dt
2 1
-1
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1 -1 4 3 2-1x. x0 1 d x 3 dt 2 1 -1

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Step 2

The eigenvectors of the matrix are given as follows.

4
1
2
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4 1 2

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Step 3

The eigenvalues of the matrix ...

1-2
-1
4
det(A- )3
2 2
-1
2
1
-1-
-(1-A)(2-2(-1-2)+1]+1[3(-1-A)+2]+4[3-2(2-2)]
=-23222+52-6
-(2-222-5A+6)
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1-2 -1 4 det(A- )3 2 2 -1 2 1 -1- -(1-A)(2-2(-1-2)+1]+1[3(-1-A)+2]+4[3-2(2-2)] =-23222+52-6 -(2-222-5A+6)

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