Edexcel FP1 2013 June — Question 2

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2013
SessionJune
TopicMatrices

2. (i) $$\mathbf { A } = \left( \begin{array} { c c } 2 k + 1 & k
- 3 & - 5 \end{array} \right) , \quad \text { where } k \text { is a constant }$$ Given that $$\mathbf { B } = \mathbf { A } + 3 \mathbf { I }$$ where \(\mathbf { I }\) is the \(2 \times 2\) identity matrix, find
  1. \(\mathbf { B }\) in terms of \(k\),
  2. the value of \(k\) for which \(\mathbf { B }\) is singular.
    (ii) Given that $$\mathbf { C } = \left( \begin{array} { r } 2
    - 3