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
L 1 ( v i ) = 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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