please prove these

Problem 1. Recall that a function L : R* - R" is (by definition) said to be a linear transformationif and only if it satisfies L(+ y) = L() + L(y) and L(ri) = rL(i) for every i, ye R* and every r E R.(a) Prove that a function L : R* - R. is a linear transformation if and only if for every choice ofscalars a, bE R and of vectors , y ( R*, it is the case that L(as + by) = al() + bL(y).(b) Suppose that L : R* - Rm and T : R* - Rm are two linear transformations such thatL(e:) = T(e;) for all i 6 {1, ..., k}. Prove that L = T; that is, prove that L(U) = T(v) for allJERK