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13. Let V and W be vector spaces, let T: V > W be linear, and let {$01,102, . . . ,wk} be a linearly

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13. Let V and W be vector spaces, let T: V > W be linear, and let {$01,102, . . . ,wk} be a linearly independent set of k vectors from R(T). Prove that if S = {U1,'Ug,...,'0k} is chosen so that T('U,g) = 102- for 2' = 1, 2, . . . ,k, then S is linearly independent. Visit goo.g1/ kmaQS2 for a solution

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