CAIE FP1 2008 November — Question 6

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2008
SessionNovember
Topic3x3 Matrices

6 The matrix \(\mathbf { A }\) is defined by $$\mathbf { A } = \left( \begin{array} { r r r r } 1 & - 1 & - 2 & - 3
- 2 & 1 & 7 & 2
- 3 & 3 & 6 & \alpha
7 & - 6 & - 17 & - 17 \end{array} \right) .$$
  1. Show that if \(\alpha = 9\) then the rank of \(\mathbf { A }\) is 2, and find a basis for the null space of \(\mathbf { A }\) in this case.
  2. Find the rank of \(\mathbf { A }\) when \(\alpha \neq 9\).