5. Let V be a finite-dimensional F-vector space, and let {₁,...,Um} be a set of m vectors in V. Show that the following two conditions are equivalent. (a) {₁,..., Um} is linearly independent. (b) For any vector space W and any vectors w₁,..., Wm E W, there exists a linear transformation T: VW such that T(vi) = w; for all i E {1, 2,...,m}.

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