| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2017 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | 3x3 Matrices |
| Type | Matrix equation solving (AB = C) |
| Difficulty | Moderate -0.5 This is a straightforward Further Maths question requiring matrix multiplication (routine calculation) followed by finding a determinant of a 2×2 matrix and solving a simple equation. While it involves 3×3 matrices, the operations are mechanical with no conceptual challenges or novel problem-solving required. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar4.03j Determinant 3x3: calculation |
2. Given that
$$\mathbf { A } = \left( \begin{array} { r r r }
3 & 1 & - 2 \\
- 1 & 0 & 5
\end{array} \right) \text { and } \mathbf { B } = \left( \begin{array} { r r }
2 & 4 \\
- k & 2 k \\
3 & 0
\end{array} \right) , \text { where } k \text { is a constant }$$
\begin{enumerate}[label=(\alph*)]
\item find the matrix $\mathbf { A B }$,
\item find the exact value of $k$ for which $\operatorname { det } ( \mathbf { A B } ) = 0$
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2017 Q2 [4]}}