| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix satisfying given equation |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question testing matrix inversion (standard 2×2 formula) and solving a matrix equation. Part (a) is routine application of the inverse formula, while part (b) requires equating matrices and solving a simple quadratic equation. The constraint a≠2 guides students away from a singular matrix. Despite being Further Maths content, the techniques are mechanical with no novel problem-solving required, making it slightly easier than average overall. |
| Spec | 4.03n Inverse 2x2 matrix |
Given that $\mathbf{X} = \begin{pmatrix} 2 & a \\ -1 & -1 \end{pmatrix}$, where $a$ is a constant, and $a \neq 2$.
\begin{enumerate}[label=(\alph*)]
\item find $\mathbf{X}^{-1}$ in terms of $a$.
[3]
\item Given that $\mathbf{X} + \mathbf{X}^{-1} = \mathbf{I}$, where $\mathbf{I}$ is the $2 \times 2$ identity matrix,
find the value of $a$.
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q7 [6]}}