$$\mathbf { B } = \left( \begin{array} { r r }
- 1 & 2
3 & - 4
\end{array} \right) , \quad \mathbf { Y } = \left( \begin{array} { r r }
4 & - 2
1 & 0
\end{array} \right)$$
(a) Find \(\mathbf { B } ^ { - 1 }\).
The transformation represented by \(\mathbf { Y }\) is equivalent to the transformation represented by \(\mathbf { B }\) followed by the transformation represented by the matrix \(\mathbf { A }\).
(b) Find \(\mathbf { A }\).
$$\mathbf { M } = \left( \begin{array} { r r }
- \sqrt { 3 } & - 1
1 & - \sqrt { 3 }
\end{array} \right)$$
The matrix \(\mathbf { M }\) represents an enlargement scale factor \(k\), centre ( 0,0 ), where \(k > 0\), followed by a rotation anti-clockwise through an angle \(\theta\) about \(( 0,0 )\).
(a) Find the value of \(k\).
(b) Find the value of \(\theta\).