Prove linear independence of orthogonal nonzero vectors

[b00tofuu]

suppose v1,...,vk are nonzero vectors with the property that vi.vj=0 whenever i is not equal to j. Prove that {v1,...,vk} is linearly independent.

 

[rochfor1]

Suppose $$\alpha_1, \ldots, \alpha_k$$ are such that $$0 = \alpha_1 v_1 + \ldots + \alpha_k v_k$$. Try taking the dot product of this equation with each of the $$v_i$$s and see what it tells you about the $$\alpha_i$$s.

 

[b00tofuu]

thank u, i got it now...