In this eqn, x(sub1), x(sub2), x(sub3) all end up equaling to 0. x(sub4) is free, shouldn't this be a dependent set then? For a homogenous soln. to have a nontrivial soln. there needs to be a free variable, there is a free variable here.

This answer says it is Independent, however, it should be dependent? What am I missing here?

Or is it because since there are pviot positions for every all columns besides column 4, that implies system is trivial? Therefore, linear ind.