Selectividad Andalucía 2001-6-A3

Determina a , b y c sabiendo que la matriz
A = \left( \begin{array}{ccc}
-3 & 1 & 1 \\
1 & a & 2 \\
-1 & b & c
\end{array} \right) verifica A \cdot \left( \begin{array}{c}
1  \\
2 \\
3
\end{array} \right)
=
\left( \begin{array}{c}
2  \\
9 \\
4
\end{array} \right) y rango(A) = 2