4. Suppose that V and W are vector spaces over a field F and let L :V → W be a function. a) Prove that L is a linear transformation if and only if L(Au + v) = \L(u) + L(v) for all λ ε F and u , v ε V. b) Let v1,….., Vn E V and A1,..., An E F. If L is a linear transformation, prove that L(A1v1 + ...+ An Vn) = A1L(v1)+...+ A„L(vn). (Hint: induction.)

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