Consider the first-order linear system $\dfrac{d\mathbf{x}}{dt} = \begin{bmatrix}-3 & -2 & \phantom{-}3\\ \phantom{-}1 & \phantom{-}0 & -3\\ \phantom{-}1 & -2 & -1\end{bmatrix}\mathbf{x}$.

1. Show that $\mathbf{x}^{(1)}(t) = \begin{bmatrix}e^{-2t}\\ e^{-2t}\\ e^{-2t}\end{bmatrix}$, $\mathbf{x}^{(2)}(t) = \begin{bmatrix}\phantom{-}e^{2t}\\ -e^{2t}\\ \phantom{-}e^{2t}\end{bmatrix}$, and $\mathbf{x}^{(3)}(t) = \begin{bmatrix}-e^{-4t}\\ \phantom{-}e^{-4t}\\ \phantom{-}e^{-4t}\end{bmatrix}$ are linearly independent solutions.
2. What is the general solution?
3. Find a particular solution satisfying the initial condition $\mathbf{x}(0) = \begin{bmatrix}0\\ 6\\ 4\end{bmatrix}$.