The state variable description of an LTI system is given by $ \left( \begin{array} x_1 \\ x_2 \\ x_3 \end{array} \right) $= $ \left( \begin{array} \ 0&a_1&0\\ 0&0&a_2\\ a_3&0&0 \end{array} \right) $$ \left( \begin{array} \ x_1\\ x_2\\ x_3 \end{array} \right) $+ $ \left( \begin{array} \ 0\\ 0\\ 1 \end{array} \right) u $ y = (1 0 0) $ \left( \begin{array} \ x_1\\ x_2\\ x_3 \end{array} \right) $ Where y is output and u is the input. The system is controllable for