CAIE FP1 2014 November — Question 5

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2014
SessionNovember
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Mark schemeDownload PDF ↗
TopicMatrices

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 \(b \neq - 5\).

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,\\
(i) find the general solution in the case $b = - 5$,\\
(ii) interpret the situation geometrically in the case $b \neq - 5$.

\hfill \mbox{\textit{CAIE FP1 2014 Q5}}