Moderate -0.5 This is a straightforward application of the determinant condition for unique solutions (det ≠ 0). Students need to form a 2×2 matrix, calculate its determinant (k² - 16), set it equal to zero, and solve to get k = ±4. While it's a Further Maths topic, it's a standard textbook exercise requiring only routine application of a well-known result with minimal algebraic manipulation.
3 By using the determinant of an appropriate matrix, find the values of \(k\) for which the simultaneous equations
$$\begin{aligned}
& k x + 8 y = 1 \\
& 2 x + k y = 3
\end{aligned}$$
do not have a unique solution.
3 By using the determinant of an appropriate matrix, find the values of $k$ for which the simultaneous equations
$$\begin{aligned}
& k x + 8 y = 1 \\
& 2 x + k y = 3
\end{aligned}$$
do not have a unique solution.
\hfill \mbox{\textit{OCR FP1 2011 Q3 [3]}}