Question: Let S be a basis for an n-dimensional vector space V. Show that if v1, v2, ... vr form a linearly independent set of vectors

Let S be a basis for an n-dimensional vector space V. Show that if v1, v2, ... vr form a linearly independent set of vectors in V, then the coordinate vectors (v1)s, (v2)s, (vr)s form a linearly independent set in Rn, and conversely.

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