Edexcel FP3 2013 June — Question 6

Exam BoardEdexcel
ModuleFP3 (Further Pure Mathematics 3)
Year2013
SessionJune
TopicInvariant lines and eigenvalues and vectors

6. It is given that \(\left( \begin{array} { l } 1
2
0 \end{array} \right)\) is an eigenvector of the matrix \(\mathbf { A }\), where $$\mathbf { A } = \left( \begin{array} { l l l } 4 & 2 & 3
2 & b & 0
a & 1 & 8 \end{array} \right)$$ and \(a\) and \(b\) are constants.
  1. Find the eigenvalue of \(\mathbf { A }\) corresponding to the eigenvector \(\left( \begin{array} { l } 1
    2
    0 \end{array} \right)\).
  2. Find the values of \(a\) and \(b\).
  3. Find the other eigenvalues of \(\mathbf { A }\).