Solved: Let V be an II -dimensional vector space with ordered basis S = {VI. V2 . . v.1
Chapter 6, Problem 31(choose chapter or problem)
Let V be an II -dimensional vector space with ordered basis S = {VI. V2 . . v.1 and let T = (WI. W l . w"1 be an ordered set of vectors in V. Prove that there is a unique linear transformation L : V __ V such that L(v;) = W i for i = l. 2 . . ... 11. [Hinl: Let L be a mapping from V into V such that L(v;) = Wi: then show how to extend L to be a linear transfonllation defin;xl on all of V. ]
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