9 The matrix \(\mathbf { D }\) is given by \(\mathbf { D } = \left( \begin{array} { l l l } 1 & 3 & 4
2 & a & 3
0 & 1 & a \end{array} \right)\).
- Find the values of \(a\) for which \(\mathbf { D }\) is singular.
- Three simultaneous equations are shown below.
$$\begin{array} { r }
x + 3 y + 4 z = 3
2 x + a y + 3 z = 2
y + a z = 0
\end{array}$$
For each of the following values of \(a\), determine whether or not there is a unique solution. If a unique solution does not exist, determine whether the equations are consistent or inconsistent.
(a) \(a = 3\)
(b) \(a = 1\)