OCR MEI FP1 2012 January — Question 9

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2012
SessionJanuary
TopicLinear transformations

9 The matrix \(\mathbf { R }\) is \(\left( \begin{array} { r r } 0 & - 1
1 & 0 \end{array} \right)\).
  1. Explain in terms of transformations why \(\mathbf { R } ^ { 4 } = \mathbf { I }\).
  2. Describe the transformation represented by \(\mathbf { R } ^ { - 1 }\) and write down the matrix \(\mathbf { R } ^ { - 1 }\).
  3. \(\mathbf { S }\) is the matrix representing rotation through \(60 ^ { \circ }\) anticlockwise about the origin. Find \(\mathbf { S }\).
  4. Write down the smallest positive integers \(m\) and \(n\) such that \(\mathbf { S } ^ { m } = \mathbf { R } ^ { n }\), explaining your answer in terms of transformations.
  5. Find \(\mathbf { R S }\) and explain in terms of transformations why \(\mathbf { R S } = \mathbf { S R }\). \section*{THERE ARE NO QUESTIONS WRITTEN ON THIS PAGE}