| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2023 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix multiplication |
| Difficulty | Moderate -0.8 This is a straightforward matrix multiplication followed by a routine determinant calculation and solving a linear equation. Part (a) requires careful arithmetic with the parameter k, and part (b) involves computing a 2×2 determinant and solving for k. While it requires accuracy, it demands only direct application of standard techniques with no problem-solving insight, making it easier than average. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar4.03j Determinant 3x3: calculation |
\begin{enumerate}
\item Given that
\end{enumerate}
$$\mathbf { A } = \left( \begin{array} { r r r }
2 & - 1 & 3 \\
- 2 & 3 & 0
\end{array} \right) \quad \text { and } \quad \mathbf { B } = \left( \begin{array} { r r }
1 & k \\
0 & - 3 \\
2 k & 2
\end{array} \right)$$
where $k$ is a non-zero constant,\\
(a) determine the matrix $\mathbf { A B }$\\
(b) determine the value of $k$ for which $\operatorname { det } ( \mathbf { A B } ) = 0$
\hfill \mbox{\textit{Edexcel F1 2023 Q1 [5]}}