| Exam Board | Edexcel |
|---|---|
| Module | F3 (Further Pure Mathematics 3) |
| Year | 2021 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | 3x3 Matrices |
| Type | Matrix inverse calculation |
| Difficulty | Standard +0.8 This is a Further Maths question requiring determinant calculation of a 3×3 matrix with a parameter (involving expansion and solving a quadratic), then finding the inverse using cofactors/adjugate method. While systematic, it demands careful algebraic manipulation across multiple steps and is more demanding than standard A-level questions, placing it moderately above average difficulty. |
| Spec | 4.03j Determinant 3x3: calculation4.03o Inverse 3x3 matrix |
$$\mathbf{M} = \begin{pmatrix}
3 & 1 & p \\
1 & 1 & 2 \\
-1 & p & 2
\end{pmatrix}$$ where $p$ is a real constant
\begin{enumerate}[label=(\alph*)]
\item Find the exact values of $p$ for which $\mathbf{M}$ has no inverse.
[4]
\end{enumerate}
Given that $\mathbf{M}$ does have an inverse,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find $\mathbf{M}^{-1}$ in terms of $p$.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel F3 2021 Q3 [9]}}