| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2022 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix inverse calculation |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths question testing standard matrix inverse formulas. Part (a) requires the 2×2 inverse formula (determinant and cofactor matrix), while part (b) applies the property (MN)^{-1} = N^{-1}M^{-1}. Both are direct applications of learned techniques with minimal algebraic manipulation, making it slightly easier than average even for Further Maths. |
| Spec | 4.03o Inverse 3x3 matrix4.03p Inverse properties: (AB)^(-1) = B^(-1)*A^(-1) |
\begin{enumerate}
\item $\mathbf { M } = \left( \begin{array} { c c } k & k \\ 3 & 5 \end{array} \right) \quad$ where $k$ is a non-zero constant\\
(a) Determine $\mathbf { M } ^ { - 1 }$, giving your answer in simplest form in terms of $k$.
\end{enumerate}
Hence, given that $\mathbf { N } ^ { - 1 } = \left( \begin{array} { c c } k & k \\ 4 & - 1 \end{array} \right)$\\
(b) determine $( \mathbf { M N } ) ^ { - 1 }$, giving your answer in simplest form in terms of $k$.
\hfill \mbox{\textit{Edexcel F1 2022 Q3 [4]}}