Question

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?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

i get the equations
\[a+3b=0\]
\[-a+b=0\]
\[-2b=0\]

Answer 7

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

Answer 8

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

Answer 9

Did you row reduce to get those equations?

Answer 10

no i just did it the donkey way

Answer 11

\[a(1,-1,0)+b(3,1,-2)=(0,0,0)\]

Answer 12

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

Answer 13

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