| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | 3x3 Matrices |
| Type | Eigenvalues and eigenvectors |
| Difficulty | Standard +0.3 This is a standard Further Maths eigenvalue question with routine procedures: finding eigenvalues via characteristic equation for a 2×2 matrix, then identifying that the invariant line corresponds to the eigenvalue λ=1 and finding its eigenvector. While it's Further Maths content (inherently harder), the techniques are algorithmic and well-practiced, making it slightly easier than average A-level difficulty overall. |
| Spec | 4.03h Determinant 2x2: calculation4.03l Singular/non-singular matrices |
$$\mathbf{M} = \begin{pmatrix} 4 & -5 \\ 6 & -9 \end{pmatrix}$$
\begin{enumerate}[label=(\alph*)]
\item Find the eigenvalues of $\mathbf{M}$. [4]
\end{enumerate}
A transformation $T: \mathbb{R}^2 \to \mathbb{R}^2$ is represented by the matrix $\mathbf{M}$. There is a line through the origin for which every point on the line is mapped onto itself under $T$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find a cartesian equation of this line. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP3 Q18 [7]}}