Answer
$=\begin{bmatrix}
4e^{4t}\\
-8e^{4t}
\end{bmatrix}$
Work Step by Step
$x'=\begin{bmatrix}
4e^{4t}\\
-8e^{4t}
\end{bmatrix}$
We have:
$x'=Ax+b$
$\begin{bmatrix}
4e^{4t}\\
-8e^{4t}
\end{bmatrix}=\begin{bmatrix}
2 & -1\\
-2 & 3
\end{bmatrix}.\begin{bmatrix}
e^{4t}\\
-2e^{4t}
\end{bmatrix}+\begin{bmatrix}
0\\
0
\end{bmatrix}$
$=\begin{bmatrix}
2e^{4t}+2e^{4t}\\
-2e^{4t}-6e^{4t}
\end{bmatrix}$
$=\begin{bmatrix}
4e^{4t}\\
-8e^{4t}
\end{bmatrix}$
