| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix satisfying given equation |
| Difficulty | Standard +0.8 This question requires finding a matrix inverse (standard F1 skill), then solving a matrix equation involving A and A^(-1). Part (b) requires algebraic manipulation to eliminate the inverse and solve a quadratic, which is non-routine and requires insight beyond standard textbook exercises. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar4.03o Inverse 3x3 matrix |
3.
$$\mathbf { A } = \left( \begin{array} { l l }
4 & - 2 \\
a & - 3
\end{array} \right)$$
where $a$ is a real constant and $a \neq 6$
\begin{enumerate}[label=(\alph*)]
\item Find $\mathbf { A } ^ { - 1 }$ in terms of $a$.
Given that $\mathbf { A } + 2 \mathbf { A } ^ { - 1 } = \mathbf { I }$, where $\mathbf { I }$ is the $2 \times 2$ identity matrix,
\item find the value of $a$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2014 Q3 [6]}}