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## Homework Statement

Solve the system.

dx/dt=[1 -4; 4 -7]*x with x(0)=[3; 2]

## Homework Equations

## The Attempt at a Solution

I am apparently not getting this at all. Can someone walk me through it? I konw I have to first find the eigenvalues and eigenvectors:

(1-λ)(-7-λ)+16=0

λ

^{2}+6λ+9=0

λ=-3,-3

So, (A-3I)C1 = 0

(A-3I)= [4 -4; 4 -4]

So, eigenvector = [1; 1]

(A-3I)C2=C1

Eigenvector = [1; 0]

And, x1= [1; 1] e

^{-3t}

x2 = ([1; 1]t + [1; 0])e

^{-3t}

So, using fundamental matrices...

F = [ e

^{-3t}(t+3) e

^{-3t}; e

^{-3t}t e

^{-3t}]

F(0) = [1 3; 1 0]

(F(0))'= [0 1; 1/3 -1/3]

So,

x(t)=F*(F(0))'*X

_{0}= [X

_{1}; X

_{2}]

Is there anything wrong with my method?

The homework asks for two answers: X

_{1}and X

_{2}and I'm not exactly sure what that is asking for. Thanks! Any help is appreciated.