A system is represented by
\(\frac{{{d^3}y\left( t \right)}}{{dt}} + \frac{{17{d^2}y\left( t \right)}}{{d{t^2}}} + \frac{{84dy\left( t \right)}}{{dt}} + 108y\left( t \right) = \frac{{du\left( t \right)}}{{dt}} + 3u\left( t \right)\)
Which of the below state variable representation represents the above system
\(\begin{array}{l} \left[ {\begin{array}{*{20}{c}} {{{\dot x}_1}}\\ {{{\dot x}_2}}\\ {{{\dot x}_3}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 2}&1&1\\ 0&{ - 9}&1\\ 0&0&{ - 6} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}}\\ {{x_3}} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 0\\ 1\\ 0 \end{array}} \right]u\\ y = \left[ {\begin{array}{*{20}{c}} 1&0&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}}\\ {{x_3}} \end{array}} \right] \end{array}\)
\(\begin{array}{l} \left[ {\begin{array}{*{20}{c}} {{{\dot x}_1}}\\ {{{\dot x}_2}}\\ {{{\dot x}_3}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 2}&3&1\\ 0&{ - 9}&1\\ 0&0&{ - 6} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}}\\ {{x_3}} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 0\\ 0\\ 1 \end{array}} \right]u\\ y = \left[ {\begin{array}{*{20}{c}} 1&0&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}}\\ {{x_3}} \end{array}} \right] \end{array}\)
\(\begin{array}{l} \left[ {\begin{array}{*{20}{c}} {{{\dot x}_1}}\\ {{{\dot x}_2}}\\ {{{\dot x}_3}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 2}&{ - 6}&1\\ 0&{ - 9}&1\\ 0&0&{ - 6} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}}\\ {{x_3}} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 0\\ 0\\ 1 \end{array}} \right]u\\ y = \left[ {\begin{array}{*{20}{c}} 1&0&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}}\\ {{x_3}} \end{array}} \right] \end{array}\)
\(\begin{array}{l} \left[ {\begin{array}{*{20}{c}} {{{\dot x}_1}}\\ {{{\dot x}_2}}\\ {{{\dot x}_3}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 2}&3&1\\ 0&{ - 9}&1\\ 0&0&{ - 6} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}}\\ {{x_3}} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 0\\ 1\\ 0 \end{array}} \right]u\\ y = \left[ {\begin{array}{*{20}{c}} 1&0&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}}\\ {{x_3}} \end{array}} \right] \end{array}\)