CAIE Further Paper 2 2020 Specimen — Question 8

Exam BoardCAIE
ModuleFurther Paper 2 (Further Paper 2)
Year2020
SessionSpecimen
Topic3x3 Matrices

8
    1. Fid bet basb le s a for which the system of equations $$\begin{array} { r l } x - 2 y - 2 z + z & 0
      2 x + ( a - 9 y - 0 z + 1 E & 0
      3 x - 6 y + 2 a z + 9 & 0 \end{array}$$ h san q sbtu in
    2. Given that \(a = - 3\), show that the system of equations in part (i) \(\mathbf { b } \mathbf { s } \mathbf { n }\) sb t in In erp et th s situation geometrically.
  1. The matrix \(\mathbf { A }\) is given by $$\mathbf { A } = \left( \begin{array} { r r r } 1 & 1 & 2
    0 & 2 & 2
    - 1 & 1 & 3 \end{array} \right)$$
    1. Find b eig le so A.
    2. Use th ch racteristic eq tiw \(\mathbf { A }\) tof id \(\mathbf { A } ^ { - 1 }\). If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.