| Exam Board | CAIE |
|---|
| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2010 |
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| Session | June |
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| Topic | 3x3 Matrices |
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10 Find the set of values of \(a\) for which the system of equations
$$\begin{aligned}
x + 4 y + 12 z & = 5
2 x + a y + 12 z & = a - 1
3 x + 12 y + 2 a z & = 10
\end{aligned}$$
has a unique solution.
Show that the system does not have any solution in the case \(a = 18\).
Given that \(a = 8\), show that the number of solutions is infinite and find the solution for which \(x + y + z = 1\).