| Exam Board | Edexcel |
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2012 |
| Session | June |
| Topic | Matrices |
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.