So I have a matrix that I am trying to find a general solution a system $x'=Ax$ where A is the matrix: $$\begin{bmatrix} 1 & 1 & 1 \\ 2 & 1 & -1 \\ -3 & 2 & 4\\ \end{bmatrix}$$ and found that the matrix has a single eigenvalue, 2, with multiplicity 3.
I've seen plenty of examples of 3x3 matrices with an eigenvalue repeated twice but never three times.
I found that the general eigenvector is $$v=c\begin{bmatrix} 0 \\ -1 \\ 1 \\ \end{bmatrix}$$ but I am at a lost as what to do next.