Find x, if $\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}x&{ - 5}&{ - 1}\end{array}} \right]\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&0&2\\0&2&1\\2&0&3\end{array}} \right]\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}x\\4\\1\end{array}} \right] = O$.

.:

$\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}x&{ - 5}&{ - 1}\end{array}} \right]\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&0&2\\0&2&1\\2&0&3\end{array}} \right]\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}x\\4\\1\end{array}} \right] = O$

$\Rightarrow$ $\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}x&{ - 5}&{ - 1}\end{array}} \right]\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}{x + 2}\\{8 + 1}\\{2x + 3}\end{array}} \right] = O$

$\Rightarrow$ $\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}x&{ - 5}&{ - 1}\end{array}} \right]\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}{x + 2}\\9\\{2x + 3}\end{array}} \right] = O$

$\Rightarrow$ $x(x + 2) - 45 - 2x - 3 = 0 \Rightarrow {x^2} - 48 = 0$

$\Rightarrow$ $x = \pm 4\sqrt 3$.