7 The matrix \(\mathbf { M }\) is given by \(\mathbf { M } = \left( \begin{array} { l l l } a & 4 & 0
0 & a & 4
2 & 3 & 1 \end{array} \right)\).
- Find, in terms of \(a\), the determinant of \(\mathbf { M }\).
- In the case when \(a = 2\), state whether \(\mathbf { M }\) is singular or non-singular, justifying your answer.
- In the case when \(a = 4\), determine whether the simultaneous equations
$$\begin{aligned}
a x + 4 y \quad = & 6
a y + 4 z & = 8
2 x + 3 y + z & = 1
\end{aligned}$$
have any solutions.