For both (a) and (b), you're pretty much spot on for proving linear dependence.
For (a), x, y, and z being independent is clear. Therefore, we need to show that u and any two of x,y, and z are linearly independent. Let and let , where . If we have (for )
then no matter what i and j are, we will always end up with the following system of equations:
which implies .
Working out part (b) is very similar.