| Exam Board | CAIE |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2014 |
| Session | November |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | 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,\\
(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}}