Edexcel FP3 — Question 18

Exam BoardEdexcel
ModuleFP3 (Further Pure Mathematics 3)
TopicInvariant lines and eigenvalues and vectors

18. $$\mathbf { M } = \left( \begin{array} { l l } 4 & - 5
6 & - 9 \end{array} \right)$$
  1. Find the eigenvalues of \(\mathbf { M }\). A transformation \(T : \mathbb { R } ^ { 2 } \rightarrow \mathbb { R } ^ { 2 }\) 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 \(T\).
  2. Find a cartesian equation of this line.
    [0pt] [P6 June 2003 Qn 3]