| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2024 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Matrices |
| Type | Non-singular matrix proof |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths question requiring calculation of a 2×2 determinant to show it's always non-zero (completing the square), then applying the standard formula for matrix inverse. While it's Further Maths content, the techniques are routine and mechanical with no novel problem-solving required, making it slightly easier than average overall. |
| Spec | 4.03l Singular/non-singular matrices4.03o Inverse 3x3 matrix |
1.
$$\mathbf { M } = \left( \begin{array} { c c }
2 k + 1 & k \\
k + 7 & k + 4
\end{array} \right) \quad \text { where } k \text { is a constant }$$
\begin{enumerate}[label=(\alph*)]
\item Show that $\mathbf { M }$ is non-singular for all real values of $k$.
\item Determine $\mathbf { M } ^ { - 1 }$ in terms of $k$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2024 Q1 [5]}}