OCR MEI Further Pure Core Specimen — Question 3

Exam BoardOCR MEI
ModuleFurther Pure Core (Further Pure Core)
SessionSpecimen
TopicInvariant lines and eigenvalues and vectors

3 Transformation M is represented by matrix \(\mathbf { M } = \left( \begin{array} { l l } 2 & 3
1 & 4 \end{array} \right)\).
  1. On the diagram in the Printed Answer Booklet draw the image of the unit square under M .
  2. (A) Show that there is a constant \(k\) such that \(\mathbf { M } \binom { x } { k x } = 5 \binom { x } { k x }\) for all \(x\).
    (B) Hence find the equation of an invariant line under M .
    (C) Draw the invariant line from part (ii) (B) on your diagram for part (i).