Trouble determining coefficients of output matrix in SS problem Couldn't find a similar problem in previous questions. I'm working on a control systems problem in state space. We are given the $A$ and $B$ matrices as well as our inputs and states. To determine BIBO stability, we need to determine our $C$ matrix, which we assume is $[c_1\;c_2\;c_3]$, and we assume our $D$ matrix is $[0]$. From earlier in the problem, we have determined that our system is marginally stable by calculating the eigenvalues of $A$ using $\text{det}(\lambda I-A)$. I'm currently stuck on finding the coefficients $c_1,c_2,c_3$, and not sure if there is something trivial I might be missing. 
For reference, the $A$ matrix is $\begin{bmatrix}0 & 1 & 0\\ 0& 0& -g\\ 0& 1/R & 0\end{bmatrix}$, where $g$ is the acceleration due to gravity and $R$ is the radius of the earth. The $B$ matrix is $\begin{bmatrix}0 & 0\\ 1 & 0\\ 0 & 1\end{bmatrix}$. 
Any help would be greatly appreciated. 
 A: To give you a clue about what is going on:
The standard state space model $(A,B,C,D)$ has 
\begin{align}
G(s) = \frac{Y(s)}{U(s)}=C(sI-A)^{-1}B+D
\end{align}
as its transfer function. The $C$ matrix does not influence stability of the entire system, $A$ does. You can however select certain stable/unstable modes, but by doing so, you could trick yourself. For example, take the system
\begin{align}&\frac{d}{dt}
\begin{pmatrix}
x_1\\
x_2
\end{pmatrix}= \begin{pmatrix}
A_{11} & 0\\
0 & A_{22}
\end{pmatrix}\begin{pmatrix}
x_1\\
x_2
\end{pmatrix} + \begin{pmatrix}
B_1\\
0
\end{pmatrix}u\\
&y = \begin{pmatrix}
C_1 & 0
\end{pmatrix}\begin{pmatrix}
x_1\\
x_2
\end{pmatrix}.
\end{align}
Now assume $A_{11}$ is stable and $A_{22}$ is unstable. Have a look at the transfer function
\begin{align}
G(s) &= \begin{pmatrix}
C_1 & 0
\end{pmatrix}
\begin{pmatrix}
(sI-A_{11})^{-1} & 0\\
0 & (sI-A_{22})^{-1}
\end{pmatrix}
\begin{pmatrix}
B_1\\
0
\end{pmatrix}\\
&=C_1(sI-A_{11})^{-1}B_1.
\end{align}
So in the end, the input-output map is BIBO stable, but internally things might blow up(state $x_2$).  
