The matrix \(\mathbf { A }\) is defined by \(\mathbf { A } = \left[ \begin{array} { c c } - 2 & c d & 3 \end{array} \right]\).
Given that the image of the point \(( 5,2 )\) under the transformation represented by \(\mathbf { A }\) is \(( - 2,1 )\), find the value of \(c\) and the value of \(d\). [0pt]
[4 marks]
The matrix \(\mathbf { B }\) is defined by \(\mathbf { B } = \left[ \begin{array} { c c } \sqrt { 2 } & \sqrt { 2 } - \sqrt { 2 } & \sqrt { 2 } \end{array} \right]\).
Show that \(\mathbf { B } ^ { 4 } = k \mathbf { I }\), where \(k\) is an integer and \(\mathbf { I }\) is the \(2 \times 2\) identity matrix.
Describe the transformation represented by the matrix \(\mathbf { B }\) as a combination of two geometrical transformations.
Find the matrix \(\mathbf { B } ^ { 17 }\).
\(6 \quad \mathrm {~A}\) curve \(C _ { 1 }\) has equation
$$\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$$