[All Steps] Solve the following initial valued problem X^prime=A X+F(t), X(0)=(-1,1) where
Question:
Solve the following initial valued problem
\[X^{\prime}=A X+F(t), \quad X(0)=(-1,1)\]where
\[A=\left[\begin{array}{cc} 1 & 2 \\ -2 & -3 \end{array}\right]\]and \(f(t)=\sin (t)\) for all \(t\) and
\[g(t)=\left\{\begin{array}{cc} t & \text { if } 0 \leq t \leq 1 \\ 2-t & \text { if } t>1 \end{array}\right.\]
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