CAIE FP1 2014 November — Question 5

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2014
SessionNovember
Topic3x3 Matrices

5 Find the value of \(a\) for which the system of equations $$\begin{aligned} & x - y + 2 z = 4
& x + a y - 3 z = b
& x - y + 7 z = 13 \end{aligned}$$ where \(a\) and \(b\) are constants, has no unique solution. Taking \(a\) as the value just found,
  1. find the general solution in the case \(b = - 5\),
  2. interpret the situation geometrically in the case \(b \neq - 5\).