7. \(\mathbf { A } = \left( \begin{array} { r r } a & - 2
- 1 & 4 \end{array} \right)\), where \(a\) is a constant.
- Find the value of \(a\) for which the matrix \(\mathbf { A }\) is singular.
$$\mathbf { B } = \left( \begin{array} { r r }
3 & - 2
- 1 & 4
\end{array} \right)$$ - Find \(\mathbf { B } ^ { - 1 }\).
The transformation represented by \(\mathbf { B }\) maps the point \(P\) onto the point \(Q\).
Given that \(Q\) has coordinates \(( k - 6,3 k + 12 )\), where \(k\) is a constant, - show that \(P\) lies on the line with equation \(y = x + 3\).