| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2025 |
| Session | February |
| Marks | 4 |
| Topic | Invariant lines and eigenvalues and vectors |
| Type | Find line of invariant points |
| Difficulty | Standard +0.3 Finding an invariant line under a matrix transformation is a standard Further Maths topic requiring solving Mv = λv for eigenvectors or using the condition y = mx maps to itself. While it involves matrix algebra and eigenvalue concepts, it's a routine 4-mark question with a well-defined procedure, making it slightly easier than average. |
| Spec | 4.03g Invariant points and lines |
Find the invariant line of the transformation of the $x$-$y$ plane represented by the matrix $\begin{pmatrix} 2 & 0 \\ 4 & -1 \end{pmatrix}$. [4]
\hfill \mbox{\textit{SPS SPS FM Pure 2025 Q8 [4]}}