OCR MEI Further Pure Core 2020 November — Question 9

Exam BoardOCR MEI
ModuleFurther Pure Core (Further Pure Core)
Year2020
SessionNovember
TopicInvariant lines and eigenvalues and vectors

9 A linear transformation of the plane is represented by the matrix \(\mathbf { M } = \left( \begin{array} { r r } 1 & - 2
\lambda & 3 \end{array} \right)\), where \(\lambda\) is a
constant. constant.
  1. Find the set of values of \(\lambda\) for which the linear transformation has no invariant lines through the origin.
  2. Given that the transformation multiplies areas by 5 and reverses orientation, find the invariant lines.