| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Matrices |
| Type | Non-singular matrix proof |
| Difficulty | Moderate -0.5 This is a straightforward Further Maths question requiring standard techniques: computing a 2×2 determinant, completing the square to show it's always positive, and applying the formula for 2×2 matrix inverse. While it's Further Maths content (making it harder than basic A-level), the methods are routine and mechanical with no problem-solving insight needed, placing it slightly below average difficulty overall. |
| Spec | 4.03h Determinant 2x2: calculation4.03n Inverse 2x2 matrix4.03o Inverse 3x3 matrix |
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\item Given that
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$$\mathbf { A } = \left( \begin{array} { c c }
k & 3 \\
- 1 & k + 2
\end{array} \right) \text {, where } k \text { is a constant }$$
(a) show that $\operatorname { det } ( \mathbf { A } ) > 0$ for all real values of $k$,\\
(b) find $\mathbf { A } ^ { - 1 }$ in terms of $k$.\\
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\hfill \mbox{\textit{Edexcel F1 2018 Q4 [5]}}