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