How to find a unknown values of state space model matrices

Question

I have the following state-space model $$ A= \begin{bmatrix} k & 0 & 1 \\ 1 & -3 & 2 \\ 0 & 0 & -4 \\ \end{bmatrix} B= \begin{bmatrix} 0 \\ 0\\ 1\\ \end{bmatrix} C = \begin{bmatrix} 0 & 1 &0 \\ \end{bmatrix} D= \begin{bmatrix} 0 \end{bmatrix} $$ Conditions for the state-space model is "k" for which the system would be:
(i) unstable.
(ii) uncontrollable.
(iii) unobservable.
So, here how can I find the unknown value "k" in the matrix A. (Any possibility to find k without using rank tests?)