# Thread: Matrices and differential equations

1. ## Matrices and differential equations

I'm a little stuck on this question, i need to work out the matrix A given the conditions, i have a picture of it here:

http://dl.dropbox.com/u/48169762/Capture.PNG

How do i know what dimensions A would be or how to correctly deduce it? it could be 3x3, 2x3, 1x3??

Thanks for any help

2. ## Re: Matrices and differential equations

Denoting $x_1=x,\;x_2=x',\;x_3=x''$ we have:

$\begin{Bmatrix}x'_1=x_2\\x'_2=x_3\\x'_3=x'''=-x_1-tx_2-(\sin t)\;x_3\end{matrix}$

So we can write:

$\begin{bmatrix}{x'_1}\\{x'_2}\\{x'_3}\end{bmatrix} = \begin{bmatrix}{0}&{1}&{0}\\{0}&{0}&{1}\\{-1}&{-t}&{-\sin t}\end{bmatrix} \begin{bmatrix}{x_1}\\{x_2}\\{x_3}\end{bmatrix}$