Matrix form of the system

Question

How to represent it as a matrix?

\begin{align} \dfrac{dx}{dt}&=4x+4y-24, \\ \dfrac{dy}{dt}&=-8x+16y+60. \end{align}

Or, at least, how to represent a single equation:

\begin{align} \dfrac{dx}{dt}&=4x+4y-24, \end{align}

?

Answer 1

$$\begin{pmatrix}\dot x\\\dot y\end{pmatrix}=\begin{pmatrix}4&4\\-8&16\end{pmatrix}\begin{pmatrix}x\\ y\end{pmatrix}+\begin{pmatrix}-24\\60\end{pmatrix}$$

Answer 2

It is a non-homogeneous linear system:

$$\begin{pmatrix}\dot x\\ \dot y\end{pmatrix}=\begin{pmatrix}4&4\\ -8&16\end{pmatrix}\begin{pmatrix} x\\ y\end{pmatrix}+\begin{pmatrix}-24\\ 60\end{pmatrix}.$$