| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2023 |
| Session | February |
| Marks | 5 |
| Topic | Invariant lines and eigenvalues and vectors |
| Type | Verify invariant line property |
| Difficulty | Standard +0.3 This is a straightforward Further Maths linear algebra question requiring students to find an eigenvector (invariant line) by solving a standard equation, then check if points are fixed. The concepts are routine for FM students, involving algebraic manipulation of matrix equations with no novel insight required. Slightly above average difficulty due to being FM content, but mechanically standard. |
| Spec | 4.03g Invariant points and lines |
\begin{enumerate}[label=(\alph*)]
\item You are given that the matrix $\begin{pmatrix} 2 & 1 \\ -1 & 0 \end{pmatrix}$ represents a transformation T.
You are given that the line with equation $y = kx$ is invariant under T.
Determine the value of k. [4]
\item Determine whether the line with equation $y = kx$ in part above is a line of invariant points under T. [1]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2023 Q4 [5]}}