If the system of linear equations \( \begin{aligned} & 2 x+2 a y+a z=0 \\ & 2 x+3 b y+b z=0 \\ & 2 x+4 c y+c…

If the system of linear equations
\(
\begin{aligned}
& 2 x+2 a y+a z=0 \\
& 2 x+3 b y+b z=0 \\
& 2 x+4 c y+c z=0
\end{aligned}
\)

where \(a, b, c \in R\) are non-zero and distinct; has a non-zero solution, then

[JEE Main 2020, 7 Jan (Shift 1)]