Edexcel F3 2020 June — Question 3

Exam BoardEdexcel
ModuleF3 (Further Pure Mathematics 3)
Year2020
SessionJune
TopicInvariant lines and eigenvalues and vectors

3. $$\mathbf { M } = \left( \begin{array} { c c c } 3 & - 4 & k
1 & - 2 & k
1 & - 5 & 5 \end{array} \right) \text { where } k \text { is a constant }$$ Given that 3 is an eigenvalue of \(\mathbf { M }\),
  1. find the value of \(k\).
  2. Hence find the other two eigenvalues of \(\mathbf { M }\).
  3. Find a normalised eigenvector corresponding to the eigenvalue 3
    .
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