Answer
$\begin{bmatrix}
x_1'\\
x_2'
\end{bmatrix}=\begin{bmatrix}
0 &e^{2t}\\
-\sin t & 0
\end{bmatrix}.\begin{bmatrix}
x_1 \\
x_2
\end{bmatrix}+\begin{bmatrix}
0\\
1
\end{bmatrix}$
Work Step by Step
The vector formulation for the given system of differential equations is:
$\begin{bmatrix}
x_1'\\
x_2'
\end{bmatrix}=\begin{bmatrix}
0 &e^{2t}\\
-\sin t & 0
\end{bmatrix}.\begin{bmatrix}
x_1 \\
x_2
\end{bmatrix}+\begin{bmatrix}
0\\
1
\end{bmatrix}$
