How can you show that S={v_1,v_2} is a linearly independent set in R^3 when you're only given 2 vectors?

Question

anonymous · Answer

(1, -1,0) and (3,1,-2) I rref them and got

anonymous · Answer

>> [1 0 -.5; 0 1 -.5]

anonymous · Answer

guess you have to show that if 
$$av_1+bv_2=0$$ then 
$$a=b=0$$ yes?

anonymous · Answer

Yeah so would I get x_1= -5 and x_2 = -.5?

anonymous · Answer

-x_1+x_2 = 0? so hence its linear independent?

anonymous · Answer

i get the equations 
$$a+3b=0$$
$$-a+b=0$$
$$-2b=0$$

anonymous · Answer

last one says b=0 and since -a+b=0 this means a = 0 as well

anonymous · Answer

really in this case it just means that one is not a multiple of the other, which it isn't

anonymous · Answer

Did you row reduce to get those equations?

anonymous · Answer

no i just did it the donkey way

anonymous · Answer

$$a(1,-1,0)+b(3,1,-2)=(0,0,0)$$

anonymous · Answer

I'm not quite following.. but it could just be me..

anonymous · Answer

I row reduced and got [1 0 -.5; 0 1 -.5]?