1. Prove that if {v1, v2, · · · , vn} is a basis for V and w1, wg, ., w, are vectors in W, not necessarily distinct, then there exists a linear transformation T : V → W such that T(v1) = w1, T(v2) - wa, , T(vn) = Wn-

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A: Since you have asked multiple questions in single request so we will be answering only first…