Let {v1, v2,..., vn} be a basis for a vector space V, and let T : V V be a linear

Chapter 8, Problem 33

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

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