OCR MEI FP1 2011 January — Question 2

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionJanuary
TopicMatrices

2 You are given that \(\mathbf { M } = \left( \begin{array} { r r } 4 & 0
- 1 & 3 \end{array} \right)\).
  1. The transformation associated with \(\mathbf { M }\) is applied to a figure of area 3 square units. Find the area of the transformed figure.
  2. Find \(\mathbf { M } ^ { - 1 }\) and \(\operatorname { det } \mathbf { M } ^ { - 1 }\).
  3. Explain the significance of \(\operatorname { det } \mathbf { M } \times \operatorname { det } \mathbf { M } ^ { - 1 }\) in terms of transformations.