Which of the following sets of vectors are linearly independent? 
Which of the following set of vectors are linearly independent?


I'm a bit confused. I think the answer(s) would be A, C, and D. I'm unsure of how to actually figure out if each one is or isn't LI/LD
 A: If $v_1,v_2\cdots v_n$ are the vectors, then they will be independent if a linear combination of them turns out to be $0$ i.e. $\sum_i \alpha_i v_i=0$ for some $\{\alpha\}_i$(at least 1 $\alpha_i\ne0$).Now you see, 
A) $v_1+(-1)v_2=0$ So DEPENDENT
B) 3 vectors, each have 1 common coordinate. So they must be dependent .(solve for yourself).
C) Independent . Satisfies definition of independence.
D) Only 1 vector. SO no question of independence
E)Dependent similar reason as (B)
F)Dependent $3\times v_1+0\times v_2=0$
A: Vectors are linearly dependent in i can express one vector as linear combination of the others. To check this you have to solve a system. In case you have 2 vectors v = (v1,v2,v3) and w = (w1,w2,w3) you have to check if a(v1,v2,v3) + b(w1,w2,w3) = (0,0,0) where a ann b are parameters to calculate. Then (av1 + bw1, av2 + bw2, aw3 + bw3) = (0,0,0). So solve the system: av1 + bw1 = 0; av2 + bw2 = 0; av3 + bw3 = 0. If a anb b exists, vectors are linearly dipendent. If not, are linearly indipendent. In your example vectors in A are linearly dependent because the two vectors are the same.
A: c and d only. a is twice the same vector and thus the second vector is in the linear span of the first.
