{v1, v2, ... , vn} is a basis for V. L1 and L2 are two linear transformations mapping V into a vectorspace W.?

Prove:

for each i = 1, 2, ... n

than L1(vi) = L2(vi)

only if L1 = L2

I can this of the concept in my head and I think I understand it but I am having trouble actually putting the proof on paper. Any help is appreciated.

Thanks

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