Question: Let {v1, . . . , vn} be a basis for a vector space V and let T: V V be a linear transformation.

Let {v1, . . . , vn} be a basis for a vector space V and let T: V → V be a linear transformation. Prove that if T (v1) = V1, T (v2) = V2 . . . , T(vn) = vn, then T is the identity transformation on V.

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