| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2021 |
| Session | October |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix satisfying given equation |
| Difficulty | Standard +0.3 This is a straightforward Further Maths matrix question requiring standard matrix inversion (using the 2×2 formula with determinant) followed by solving a matrix equation by equating corresponding elements. While it involves algebraic manipulation and is from Further Maths, the techniques are routine and the problem-solving demand is modest—slightly easier than average for A-level overall but typical for F1. |
| Spec | 4.03n Inverse 2x2 matrix4.03o Inverse 3x3 matrix |
1.
$$\mathbf { A } = \left( \begin{array} { r r }
3 & a \\
- 2 & - 2
\end{array} \right)$$
where $a$ is a non-zero constant and $a \neq 3$
\begin{enumerate}[label=(\alph*)]
\item Determine $\mathbf { A } ^ { - 1 }$ giving your answer in terms of $a$.
Given that $\mathbf { A } + \mathbf { A } ^ { - 1 } = \mathbf { I }$ where $\mathbf { I }$ is the $2 \times 2$ identity matrix,
\item determine the value of $a$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2021 Q1 [5]}}