10 The matrix \(\mathbf { A }\) is given by \(\mathbf { A } = \left( \begin{array} { l l l } a & 2 & 1
1 & 3 & 2
4 & 1 & 1 \end{array} \right)\).
- Find the value of \(a\) for which \(\mathbf { A }\) is singular.
- Given that \(\mathbf { A }\) is non-singular, find \(\mathbf { A } ^ { - 1 }\) and hence solve the equations
$$\begin{aligned}
a x + 2 y + z & = 1
x + 3 y + 2 z & = 2
4 x + y + z & = 3
\end{aligned}$$