Let S be a basis for an n-dimensional vector space V. Show that if v[sub]1[/sub], v[sub]2[/sub], .., v[sub]r[/sub] form a linearly independent set of vectors i V, then the coordinate vectors (v[sub]1[/sub])s, (v[sub]2[/sub])s, .., (v[sub]r[/sub])s form a linearly independent set in R[sup]n[/sup], and conversely.
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