Let 01, 02, 03 be three nonzero vectors in a vector space V. Suppose that V1, V2, V3 are orthogonal relative to the (non-degenerate and positive definite) scalar product (): V x V → R, i.e., (V1, V₂) = 0, (v1,v3) = 0, (V2, V3) = 0. (1) Show that 01, 02, 03 are necessarily linearly independent.

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