Eigenvalue Method

  • Thread starter jrsweet
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Homework Statement


solve the system dx/dt = [12 -6; 6 -3] with the initial value x(0) = [12; 9]


Homework Equations





The Attempt at a Solution


I know I need to find the Eigenvalues but then I get a little confused from there.

(λ-3)(λ+3)=0
λ=3, -3
 

Answers and Replies

  • #2
HallsofIvy
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Homework Statement


solve the system dx/dt = [12 -6; 6 -3] with the initial value x(0) = [12; 9]
A assume you mean "dx/dt= [12 -6; 6 -3]x" or, in Latex,
[tex]\frac{dX}{dt}= \frac{d\begin{bmatrix}x \\ y\end{bmatrix}}{dt}= \begin{bmatrix}12 & -6 \\ 6 & -3\end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}[/tex]


Homework Equations





The Attempt at a Solution


I know I need to find the Eigenvalues but then I get a little confused from there.

(λ-3)(λ+3)=0
λ=3, -3
That's wrong. Show us how you got the eigenvalue equation.
 

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