Show that the set [(3,-2,4),(1,2,-1), (-6,4,-8) is linearly dependent by writing a non-trivial liner combination of the vectors that equals the zero vector.
After some calculations I got t1=2, t2=0 and t3=1, but its my understanding that if a set is dependent, none of the t's can equal 0. Is this correct?
Your answer is correct.
The fact that t2=0 means that t1 and t3 are linearly dependent, resulting in two independent variables in R3. This is still a linear dependent set.