SPS SPS FM Pure 2023 September — Question 13

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2023
SessionSeptember
TopicLinear transformations

13. The matrix \(\mathbf { M }\) is given by $$\mathbf { M } = \left( \begin{array} { r r } - \frac { 3 } { 5 } & \frac { 4 } { 5 }
\frac { 4 } { 5 } & \frac { 3 } { 5 } \end{array} \right)$$
  1. The diagram below shows the unit square \(O A B C\). The image of the unit square under the transformation represented by M is \(O A ^ { \prime } B ^ { \prime } C ^ { \prime }\). Draw and clearly label \(O A ^ { \prime } B ^ { \prime } C ^ { \prime }\).
    \includegraphics[max width=\textwidth, alt={}, center]{c9751c50-bab1-43fa-b580-909e1ce06a9d-28_778_1095_513_557}
  2. Find the equation of the line of invariant points of this transformation.
    1. Find the determinant of M .
    2. Describe briefly how this value relates to the transformation represented by M .
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