9 The matrix \(\mathbf { A }\) is given by \(\mathbf { A } = \left( \begin{array} { r r r } a & a & - 1
0 & a & 2
1 & 2 & 1 \end{array} \right)\).
- Find, in terms of \(a\), the determinant of \(\mathbf { A }\).
- Three simultaneous equations are shown below.
$$\begin{aligned}
a x + a y - z & = - 1
a y + 2 z & = 2 a
x + 2 y + z & = 1
\end{aligned}$$
For each of the following values of \(a\), determine whether the equations are consistent or inconsistent. If the equations are consistent, determine whether or not there is a unique solution.
(a) \(a = 0\)
(b) \(a = 1\)
(c) \(a = 2\)