The linear system is:
$$\begin{aligned} 3x +2y + z &= 0\\ 6x + 4y + \lambda z &= 0\end{aligned}$$
I have had a few attempts at this with little success. I have also seen similar questions asked here but I can not wrap my head around them. I understand a consistent system requires at least 1 solution set. So I have been trying to equate λ to the remnants of a reduced system but i have had no luck. Any assistance is appreciated.
Multiplying the first equation by $-2$ and adding to the second one we get $$-2z+\lambda z=0$$ Can you finish?