7.
$$\mathbf { P } = \left( \begin{array} { c c }
\frac { 5 } { 13 } & - \frac { 12 } { 13 }
\frac { 12 } { 13 } & \frac { 5 } { 13 }
\end{array} \right)$$
- Describe fully the single geometrical transformation \(U\) represented by the matrix \(\mathbf { P }\).
The transformation \(V\), represented by the \(2 \times 2\) matrix \(\mathbf { Q }\), is a reflection in the line with equation \(y = x\)
- Write down the matrix \(\mathbf { Q }\).
Given that the transformation \(V\) followed by the transformation \(U\) is the transformation \(T\), which is represented by the matrix \(\mathbf { R }\),
- find the matrix \(\mathbf { R }\).
- Show that there is a value of \(k\) for which the transformation \(T\) maps each point on the straight line \(y = k x\) onto itself, and state the value of \(k\).
\includegraphics[max width=\textwidth, alt={}, center]{38217fcb-8f26-49ac-9bb1-61c2f304006e-17_2261_54_312_34}
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