$$\mathbf { P } = \left( \begin{array} { r r }
0 & - 1
- 1 & 0
\end{array} \right)$$
The matrix \(\mathbf { P }\) represents a geometrical transformation \(U\)
- Describe \(U\) fully as a single geometrical transformation.
The transformation \(V\), represented by the \(2 \times 2\) matrix \(\mathbf { Q }\), is a rotation through \(240 ^ { \circ }\) anticlockwise about the origin followed by an enlargement about ( 0,0 ) with scale factor 6
- Determine the matrix \(\mathbf { Q }\), giving each entry in exact numerical form.
Given that \(U\) followed by \(V\) is the transformation \(T\), which is represented by the matrix \(\mathbf { R }\)
- determine the matrix \(\mathbf { R }\)
(ii) The transformation \(W\) is represented by the matrix
$$\left( \begin{array} { c c }
- 2 & 2 \sqrt { 3 }
2 \sqrt { 3 } & 2
\end{array} \right)$$
Show that there is a real number \(\lambda\) for which \(W\) maps the point \(( \lambda , 1 )\) onto the point ( \(4 \lambda , 4\) ), giving the exact value of \(\lambda\)
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