5.
$$\mathbf { P } = \left( \begin{array} { r r }
\frac { 1 } { 2 } & - \frac { \sqrt { 3 } } { 2 }
\frac { \sqrt { 3 } } { 2 } & \frac { 1 } { 2 }
\end{array} \right)$$
The matrix \(\mathbf { P }\) represents the transformation \(U\)
- Give a full description of \(U\) as a single geometrical transformation.
The transformation \(V\), represented by the \(2 \times 2\) matrix \(\mathbf { Q }\), is a reflection in the line \(y = - x\)
- Write down the matrix \(\mathbf { Q }\)
The transformation \(U\) followed by the transformation \(V\) is represented by the matrix \(\mathbf { R }\)
- Determine the matrix \(\mathbf { R }\)
The transformation \(W\) is represented by the matrix \(3 \mathbf { R }\)
The transformation \(W\) maps a triangle \(T\) to a triangle \(T ^ { \prime }\)
The transformation \(W ^ { \prime }\) maps the triangle \(T ^ { \prime }\) back to the original triangle \(T\)
- Determine the matrix that represents \(W ^ { \prime }\)