7.
$$A = \left( \begin{array} { c c }
- \frac { \sqrt { 3 } } { 2 } & - \frac { 1 } { 2 }
\frac { 1 } { 2 } & - \frac { \sqrt { 3 } } { 2 }
\end{array} \right)$$
- Determine the matrix \(\mathbf { A } ^ { 2 }\)
- Describe fully the single geometrical transformation represented by the matrix \(\mathbf { A } ^ { 2 }\)
- Hence determine the smallest positive integer value of \(n\) for which \(\mathbf { A } ^ { n } = \mathbf { I }\)
The matrix \(\mathbf { B }\) represents a stretch scale factor 4 parallel to the \(x\)-axis.
- Write down the matrix \(\mathbf { B }\)
The transformation represented by matrix \(\mathbf { A }\) followed by the transformation represented by matrix \(\mathbf { B }\) is represented by the matrix \(\mathbf { C }\)
- Determine the matrix \(\mathbf { C }\)
The parallelogram \(P\) is transformed onto the parallelogram \(P ^ { \prime }\) by the matrix \(\mathbf { C }\)
- Given that the area of parallelogram \(P ^ { \prime }\) is 20 square units, determine the area of parallelogram \(P\)