I want to convert this 2nd order differential equation into first order differential equation system.(matrix form).

$y''-3y'-4y+12t-2=0$.

Answer: My attempt is putting $x_1=y, x'_1=y'=x_2,x'_2=y''$ so i get $x'_2=3x'_1-4x_1+12t-2=0$

Answer provided to me is $\vec{x'}=\small\begin{pmatrix}1&2\\3&2\end {pmatrix}$$\vec{x}+t \small\begin{pmatrix}2\\-4\end{pmatrix}$

How to arrive at the answer?