Edexcel F3 2017 June — Question 4

Exam BoardEdexcel
ModuleF3 (Further Pure Mathematics 3)
Year2017
SessionJune
TopicInvariant lines and eigenvalues and vectors

4. $$\mathbf { M } = \left( \begin{array} { l l l } 1 & 1 & 3
1 & 5 & 1
3 & 1 & 1 \end{array} \right)$$
  1. Show that 6 is an eigenvalue of the matrix \(\mathbf { M }\) and find the other two eigenvalues of \(\mathbf { M }\).
  2. Find a normalised eigenvector corresponding to the eigenvalue 6