Edexcel F3 2018 June — Question 2

Exam BoardEdexcel
ModuleF3 (Further Pure Mathematics 3)
Year2018
SessionJune
TopicInvariant lines and eigenvalues and vectors

2. $$\mathbf { A } = \left( \begin{array} { l l } 3 & 2
2 & 6 \end{array} \right)$$
  1. Find the eigenvalues and corresponding normalised eigenvectors of the matrix \(\mathbf { A }\).
  2. Write down a matrix \(\mathbf { P }\) and a diagonal matrix \(\mathbf { D }\) such that \(\mathbf { P } ^ { \mathrm { T } } \mathbf { A P } = \mathbf { D }\).