Edexcel F3 2023 June — Question 5

Exam BoardEdexcel
ModuleF3 (Further Pure Mathematics 3)
Year2023
SessionJune
Topic3x3 Matrices

5. $$\mathbf { M } = \left( \begin{array} { r r r } 1 & 2 & k
- 1 & - 3 & 4
2 & 6 & - 8 \end{array} \right) \quad \text { where } k \text { is a constant }$$ Given that \(\mathbf { M }\) has a repeated eigenvalue, determine
  1. the possible values of \(k\),
  2. all corresponding eigenvalues of \(\mathbf { M }\) for each value of \(k\).