Conditions for linear independence

[csc2iffy]

Homework Statement

Under what conditions on the numbers a and b are the vectors (1,a), (1,b) linearly independent in R2?

Homework Equations

The Attempt at a Solution

x(1,a)+y(1,b)=(0,0)
(x,ax)+(y,by)=(0,0)
(x+y, ax+by)=(0,0)
x+y=0, ax+by=0
x=-y, ax=-by
unsure where to go from here...

 

[Deveno]

what does it mean for two vectors to be linearly independent?

(hint: the answer is NOT:

there exist c₁,c₂ such that c₁v₁+c₂v₂ = 0).

 

[HallsofIvy]

what does it mean for two vectors to be linearly independent?

(hint: the answer is NOT:

there exist c₁,c₂ such that c₁v₁+c₂v₂ = 0).

Good hint!