For what values of $x:\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&2&1\end{array}} \right]\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&2&0\\2&0&1\\1&0&2\end{array}} \right]\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}0\\2\\x\end{array}} \right] = O?$

.:

$\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&2&1\end{array}} \right]\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&2&0\\2&0&1\\1&0&2\end{array}} \right]\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}0\\2\\x\end{array}} \right] = O$

$\Rightarrow$ $\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}{1 + 4 + 1}&{2 + 0 + 0}&{0 + 2 + 0}\end{array}} \right]\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}0\\2\\x\end{array}} \right] = O$

$\Rightarrow$ $[\begin{array}{rrrrrrrrrrrrrrrrrrrr}6&2&4\end{array}]\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}0\\2\\x\end{array}} \right] = O$

$0 + 4 + 4x = 0 \Rightarrow 4\left( {x + 1} \right) = 0 \Rightarrow x + 1 = 0 \Rightarrow x = - 1.$