Let {v1, ..., vn} be a basis for a vector space V, and let L1 and L2 be two linear transformations mapping V into a vector space W. Show that if L1 (vi) = L2 (vi) for each i = 1, ..., n, then L1 = L2 [i. e., show that L1 (v) = L2 (v) for all v ∈ V].
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