| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Matrices |
| Type | Solving matrix equations for unknown matrix |
| Difficulty | Standard +0.3 This is a straightforward Further Maths matrix question requiring standard techniques: finding a 2×2 inverse using the determinant formula, then solving for X by post-multiplying both sides by A^(-1). The algebra simplifies nicely with the parameters p and q canceling out. While it's Further Maths content (making it slightly above average), it's a routine textbook exercise with no conceptual challenges or novel insights required. |
| Spec | 4.03n Inverse 2x2 matrix4.03o Inverse 3x3 matrix |
4.
$$\mathbf { A } = \left( \begin{array} { c c }
2 p & 3 q \\
3 p & 5 q
\end{array} \right)$$
where $p$ and $q$ are non-zero real constants.
\begin{enumerate}[label=(\alph*)]
\item Find $\mathbf { A } ^ { - 1 }$ in terms of $p$ and $q$.
Given $\mathbf { X A } = \mathbf { B }$, where
$$\mathbf { B } = \left( \begin{array} { c c }
p & q \\
6 p & 11 q \\
5 p & 8 q
\end{array} \right)$$
\item find the matrix $\mathbf { X }$, giving your answer in its simplest form.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2018 Q4 [7]}}