5.
$$\mathbf { A } = \left( \begin{array} { r r }
- \frac { 1 } { 2 } & - \frac { \sqrt { 3 } } { 2 }
\frac { \sqrt { 3 } } { 2 } & - \frac { 1 } { 2 }
\end{array} \right)$$
- Describe fully the single geometrical transformation \(U\) represented by the matrix \(\mathbf { A }\).
The transformation \(V\), represented by the \(2 \times 2\) matrix \(\mathbf { B }\), is a reflection in the line \(y = - x\)
- Write down the matrix \(\mathbf { B }\).
Given that \(U\) followed by \(V\) is the transformation \(T\), which is represented by the matrix \(\mathbf { C }\), (c) find the matrix \(\mathbf { C }\).
- Show that there is a real number \(k\) for which the point \(( 1 , k )\) is invariant under \(T\).
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