Solve Eigenvalue Method for dx/dt=[12 -6; 6 -3] w/x(0)=[12; 9]

[jrsweet]

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

 

[HallsofIvy]

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,
\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}

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.