OCR MEI Further Pure Core 2021 November — Question 9

Exam BoardOCR MEI
ModuleFurther Pure Core (Further Pure Core)
Year2021
SessionNovember
TopicLinear transformations

9 The transformation Too the plane has associated matrix \(\mathbf { M }\), where \(\mathbf { M } = \left( \begin{array} { l l } - 1 & 0
- 2 & 1 \end{array} \right)\).
  1. On the grid in the Printed Answer Booklet, plot the image \(\mathrm { OA } ^ { \prime } \mathrm { B } ^ { \prime } \mathrm { C } ^ { \prime }\) of the unit square OABC under the transformation T.
    1. Calculate the value of \(\operatorname { det } \mathbf { M }\).
    2. Explain the significance of the value of \(\operatorname { det } \mathbf { M }\) in relation to the image \(\mathrm { OA } ^ { \prime } \mathrm { B } ^ { \prime } \mathrm { C } ^ { \prime }\).
  2. T is equivalent to a sequence of two transformations of the plane.
    1. Specify fully two transformations equivalent to T .
    2. Use matrices to verify your answer.