# Eigenvalue Method

1. Nov 1, 2009

### jrsweet

1. The problem statement, all variables and given/known data
solve the system dx/dt = [12 -6; 6 -3] with the initial value x(0) = [12; 9]

2. Relevant equations

3. 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

2. Nov 2, 2009

### HallsofIvy

Staff Emeritus
A assume you mean "dx/dt= [12 -6; 6 -3]x" or, in Latex,
$$\frac{dX}{dt}= \frac{d\begin{bmatrix}x \\ y\end{bmatrix}}{dt}= \begin{bmatrix}12 & -6 \\ 6 & -3\end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}$$

That's wrong. Show us how you got the eigenvalue equation.