If the system of linear equations $x + 2ay + az = 0;$ $x + 3by + bz = 0;\,\,x + 4cy + cz = 0;$ has a non - zero solution, then $a, b, c$.

Question

If the system of linear equations
$x + 2ay + az = 0;$ $x + 3by + bz = 0;\,\,x + 4cy + cz = 0;$
has a non - zero solution, then $a, b, c$.

satisfy $a+2b+3c=0$