Solve the following homogeneous linear systems.
(a)
$$
\begin{aligned}
x+y-2 z & =0, \\
-x+4 y-3 z & =0 .
\end{aligned}
$$
(d)
$$
\begin{aligned}
x+2 y-2 z+w & =0, \\
-3 x+z-2 w & =0 .
\end{aligned}
$$
(b)
$$
2 x+3 y-z=0,
$$
$$
-x+y-4 z=0,
$$
(c)
$$
x-3 y+3 z=0 \text {. }
$$
$$
-x+3 y-2 z+w=0,
$$
(e) $-2 x+5 y+z-2 w=0$,
$$
3 x-8 y+z-4 w=0 \text {. }
$$
$-2 x+2 y-6 z=0$,
$x+3 y+3 z=0$.
$$
-y+z=0,
$$
$$
2 x-3 w=0,
$$
(f)
$$
\begin{aligned}
& x+y-2 w=0, \\
& y-3 z+w=0 .
\end{aligned}
$$