Edexcel FP1 2012 June — Question 2

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2012
SessionJune
TopicMatrices

2. (a) Given that $$\mathbf { A } = \left( \begin{array} { l l l } 3 & 1 & 3
4 & 5 & 5 \end{array} \right) \quad \text { and } \quad \mathbf { B } = \left( \begin{array} { r r } 1 & 1
1 & 2
0 & - 1 \end{array} \right)$$ find \(\mathbf { A B }\).
(b) Given that $$\mathbf { C } = \left( \begin{array} { l l } 3 & 2
8 & 6 \end{array} \right) , \quad \mathbf { D } = \left( \begin{array} { r r } 5 & 2 k
4 & k \end{array} \right) , \text { where } k \text { is a constant }$$ and $$\mathbf { E } = \mathbf { C } + \mathbf { D }$$ find the value of \(k\) for which \(\mathbf { E }\) has no inverse.