Find the value of x , if $\displaystyle \left[\begin{array}{lll}1 & \mathrm{x} & 1\end{array}\right]\left[\begin{array}{ccc}1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2\end{array}\right]\left[\begin{array}{l}1 \\ 2 \\ \mathrm{x}\end{array}\right]=\mathrm{O}$.

\[\begin{gathered} {\left[\begin{array}{lll} 1 & \mathrm{x} & 1 \end{array}\right]\left[\begin{array}{ccc} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{array}\right]\left[\begin{array}{l} 1 \\ 2 \\ \mathrm{x} \end{array}\right]=0} \\ {\left[\begin{array}{lll} 1 & \mathrm{x} & 1 \end{array}\right]\left[\begin{array}{c} 7+2 \mathrm{x} \\ 12+\mathrm{x} \\ 21+2 \mathrm{x} \end{array}\right]=0} \\ \mathrm{x}^{2}+16 \mathrm{x}+28=0 \\ \Rightarrow(\mathrm{x}+14)(\mathrm{x}+2)=0 \\ \Rightarrow \mathrm{x}=-14, \mathrm{x}=-2 \end{gathered} \]