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(v1) = L2(v1)
for each i = I,... ,11 then L1 = L2 [i.e., show that L1(v) = L2(v) for all v ∈ V).