| Exam Board | OCR |
|---|
| Module | FP1 (Further Pure Mathematics 1) |
|---|
| Year | 2009 |
|---|
| Session | January |
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| Topic | 3x3 Matrices |
|---|
5 By using the determinant of an appropriate matrix, or otherwise, find the value of \(k\) for which the simultaneous equations
$$\begin{aligned}
2 x - y + z & = 7
3 y + z & = 4
x + k y + k z & = 5
\end{aligned}$$
do not have a unique solution for \(x , y\) and \(z\).