8. (a) Solve \mathbf{x}^{\prime \prime}=\left[\begin{array}{cc} -3 & 1 \\ 2 & -2 \end{array}\right] \mathbf{x} (b) Read Section 3.6.3 on Forced Oscillations in the textbook (page 121-122). Follow the given procedure

to find a particular solution of \mathbf{x}^{\prime \prime}=\left[\begin{array}{cc} -3 & 1 \\ 2 & -2 \end{array}\right] \mathbf{x}+\left[\begin{array}{l} 0 \\ 2 \end{array}\right] \cos (4 t) Note: the procedure for finding a particular solution is also detailed at the end of the Section 3.6 lecture notes posted on D2L. (c) Using your responses to part (a) and (b), write a general solution to \mathbf{x}^{\prime \prime}=\left[\begin{array}{cc} -3 & 1 \\ 2 & -2 \end{array}\right] \mathbf{x}+\left[\begin{array}{l} 0 \\ 2 \end{array}\right] \cos (4 t)