Find the general solution to the following second order systems:
(a) $\frac{d^2 u}{d t^2}=-3 u+2 v, \frac{d^2 v}{d t^2}=2 u-3 v$.
(b) $\frac{d^2 u}{d t^2}=-11 u-2 v, \frac{d^2 v}{d t^2}=-2 u-14 v$.
(c) $\frac{d^2 \mathbf{u}}{d t^2}+\left(\begin{array}{lll}1 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 9\end{array}\right) \mathbf{u}=\mathbf{0}$
(d) $\frac{d^2 \mathbf{u}}{d t^2}=\left(\begin{array}{rrr}-6 & 4 & -1 \\ 4 & -6 & 1 \\ -1 & 1 & -11\end{array}\right) \mathbf{u}$.