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