| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2016 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Matrices |
| Type | Non-singular matrix proof |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question requiring routine determinant calculation (completing the square to show it's always positive) and standard 2×2 matrix inversion formula. Both parts are direct applications of basic matrix techniques with no problem-solving insight needed. |
| Spec | 4.03h Determinant 2x2: calculation4.03n Inverse 2x2 matrix |
4. Given that
$$\mathbf { A } = \left( \begin{array} { c c }
k & 3 \\
- 1 & k + 2
\end{array} \right) \text {, where } k \text { is a constant }$$
\begin{enumerate}[label=(\alph*)]
\item show that $\operatorname { det } ( \mathbf { A } ) > 0$ for all real values of $k$,
\item find $\mathbf { A } ^ { - 1 }$ in terms of $k$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2016 Q4 [5]}}