Maths with David

    9321. FP1. Matrices. Past Exam Questions

    1. November 2025 (9231/12). Question 4
      • Let k and m be non-zero constants. The matrices A, B and C are given by A = \begin{pmatrix} 0 & 1 \\ -1 & 1 \\ 1 & 1 \end{pmatrix} , B = \begin{pmatrix} k & 0 \\ 0 & m \end{pmatrix} and C = \begin{pmatrix} 2 & -1 & 1 \\ 1 & 1 & 2 \end{pmatrix}
      • (a) Give full details of the geometrical transformation in the x-y plane represented by the matrix B in each of the following cases:
        • (i) m = 1 [2 marks]
        • (ii) m = k [2 marks]
      • (b) Show that the matrix ABC is singular. [6 marks]