- A system of three equations is defined by
$$\begin{aligned}
k x + 3 y - z & = 3
3 x - y + z & = - k
- 16 x - k y - k z & = k
\end{aligned}$$
where \(k\) is a positive constant.
Given that there is no unique solution to all three equations,
- show that \(k = 2\)
Using \(k = 2\)
- determine whether the three equations are consistent, justifying your answer.
- Interpret the answer to part (b) geometrically.