| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | 3x3 Matrices |
| Type | Matrix inverse calculation |
| Difficulty | Standard +0.3 This is a straightforward FP3 matrix question testing standard techniques: computing a 3×3 determinant (routine expansion), finding a matrix inverse using cofactors (mechanical but lengthy), and solving a matrix equation. All parts are textbook exercises requiring careful calculation but no problem-solving insight. Slightly above average difficulty due to the algebraic parameter u and the computational length, but well within typical Further Maths expectations. |
| Spec | 4.03j Determinant 3x3: calculation4.03o Inverse 3x3 matrix4.03r Solve simultaneous equations: using inverse matrix |
$$\mathbf{A} = \begin{pmatrix} 3 & 1 & -1 \\ 1 & 1 & 1 \\ 5 & 3 & u \end{pmatrix}, \quad u \neq 1.$$
\begin{enumerate}[label=(\alph*)]
\item Show that $\det \mathbf{A} = 2(u - 1)$. [2]
\item Find the inverse of $\mathbf{A}$. [6]
\end{enumerate}
The image of the vector $\begin{pmatrix} a \\ b \\ c \end{pmatrix}$ when transformed by the matrix $\begin{pmatrix} 3 & 1 & -1 \\ 1 & 1 & 1 \\ 5 & 3 & 6 \end{pmatrix}$ is $\begin{pmatrix} 3 \\ 1 \\ 6 \end{pmatrix}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the values of $a$, $b$ and $c$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP3 Q19 [11]}}