a
(a) $\left[ {\begin{array}{*{20}{c}}1&2&3\\3&1&2\\2&3&1\end{array}} \right]\,\,\left[ \begin{array}{l}x\\y\\z\end{array} \right] = \left[ {\begin{array}{*{20}{c}}4\\0\\{ - 1}\end{array}\,\,\begin{array}{*{20}{c}}{ - 2}\\{ - 6}\\2\end{array}} \right]\,\left[ \begin{array}{l}2\\1\end{array} \right]\,$
$\begin{array}{l}\,\,\,\,\,\,\,\,\,\,\,\,\,x + 2y + 3z = 6\\\, \Rightarrow \,\,\,\,\,3x + y + 2z = - \,6\\\,{\rm{ }}2x + 3y + z = 0\end{array}$
On Simplification the above equation, we get the required result i.e.,
$x = - 4,\,y = 2,\,z = 2$.