CAIE FP1 2018 November — Question 2

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2018
SessionNovember
TopicInvariant lines and eigenvalues and vectors

2 It is given that $$\mathbf { A } = \left( \begin{array} { r r r } 2 & 3 & 1
0 & - 2 & 1
0 & 0 & 1 \end{array} \right)$$
  1. Find the eigenvalue of \(\mathbf { A }\) corresponding to the eigenvector \(\left( \begin{array} { l } 1
    0
    0 \end{array} \right)\).
  2. Write down the negative eigenvalue of \(\mathbf { A }\) and find a corresponding eigenvector.
  3. Find an eigenvalue and a corresponding eigenvector of the matrix \(\mathbf { A } + \mathbf { A } ^ { 6 }\).