Let V be a vector space with basis{v1, v2,..., vk } and suppose T : V W is a linear
Chapter 6, Problem 36(choose chapter or problem)
Let V be a vector space with basis{v1, v2,..., vk } and suppose T : V W is a linear transformation such that T (vi) = 0 for each i = 1, 2,..., k. Prove that T is the zero transformation; that is, T (v) = 0 for each v V.Let T1 : V W and T2 : V W be linear transformations, and let c be a scalar. We define the sum T1 + T2 and the scalar product cT1 by (T1 + T2)(v) = T1(v) + T2(v) and (cT1)(v) = cT1(v) for all v V. The remaining problems in this section consider the properties of these mappings.
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