Is {v1,...,vk} Linearly Independent Given vi.vj=0 When i≠j?

[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_is and see what it tells you about the \alpha_is.

 

[b00tofuu]

thank u, i got it now...