SPS SPS FM Pure 2021 June — Question 13

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2021
SessionJune
TopicLinear transformations

13. $$\mathbf { A } = \left( \begin{array} { c c } 2 & a
a - 4 & b \end{array} \right)$$ where \(a\) and \(b\) are non-zero constants.
Given that the matrix \(\mathbf { A }\) is self-inverse,
  1. determine the value of \(b\) and the possible values for \(a\). The matrix \(\mathbf { A }\) represents a linear transformation \(M\).
    Using the smaller value of \(a\) from part (a),
  2. show that the invariant points of the linear transformation \(M\) form a line, stating the equation of this line.
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