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

Chapter 8, Problem 32

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Let {v1, v2,..., vn} be a basis for a vector space V, and let T : V W be a linear transformation. Prove that if T(v1) = T(v2) == T(vn) = 0 then T is the zero transformation.

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