7. (i)
$$\mathbf { A } = \left( \begin{array} { r r }
- 1 & 0
0 & 1
\end{array} \right)$$
- Describe fully the single transformation represented by the matrix \(\mathbf { A }\).
The matrix \(\mathbf { B }\) represents a stretch, scale factor 3 , parallel to the \(x\)-axis.
- Find the matrix \(\mathbf { B }\).
(ii)
$$\mathbf { M } = \left( \begin{array} { r r }
- 4 & 3
- 3 & - 4
\end{array} \right)$$
The matrix \(\mathbf { M }\) represents an enlargement with scale factor \(k\) and centre ( 0,0 ), where \(k > 0\), followed by a rotation anticlockwise through an angle \(\theta\) about ( 0,0 ). - Find the value of \(k\).
- Find the value of \(\theta\), giving your answer in radians to 2 decimal places.
- Find \(\mathbf { M } ^ { - 1 }\)