Find P and D for A = PDP⁻¹

Questions asking to find matrices P and diagonal matrix D such that A = PDP⁻¹ (standard diagonalization of matrix A)

26 questions · Standard +0.6

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AQA Further Paper 2 2022 June Q11
9 marks Standard +0.3
11
  1. Find the eigenvalues and corresponding eigenvectors of the matrix $$\mathbf { M } = \left[ \begin{array} { c c } \frac { 5 } { 2 } & - \frac { 3 } { 2 } \\ - \frac { 3 } { 2 } & \frac { 13 } { 2 } \end{array} \right]$$ 11
    1. Describe how the directions of the invariant lines of the transformation represented by \(\mathbf { M }\) are related to each other. Fully justify your answer.
      [0pt] [2 marks]
      11
  3. (ii) Describe fully the transformation represented by \(\mathbf { M }\)