- The matrix \(\mathbf { A }\) is defined by
$$\mathbf { A } = \left( \begin{array} { c c }
3 k & 4 k - 1
2 & 6
\end{array} \right)$$
where \(k\) is a constant.
- Determine the value of \(k\) for which \(\mathbf { A }\) is singular.
Given that \(\mathbf { A }\) is non-singular,
- determine \(\mathbf { A } ^ { - 1 }\) in terms of \(k\), giving your answer in simplest form.
(ii) The matrix \(\mathbf { B }\) is defined by
$$\mathbf { B } = \left( \begin{array} { l l }
p & 0
0 & q
\end{array} \right)$$
where \(p\) and \(q\) are integers.
State the value of \(p\) and the value of \(q\) when \(\mathbf { B }\) represents - an enlargement about the origin with scale factor - 2
- a reflection in the \(y\)-axis.