Suppose that U, V are n dimensional vector spaces over a field F, and let spanU u 1 , , u n Suppose further that X U V and Y V U are linear transformations such that Xu i Yu i for i 1, , n Prove X Y

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Question: Suppose that U, V are n-dimensional vector spaces over a field F, and let spanU = {u 1 , ..., u n }. Suppose further

Suppose that U, V are n-dimensional vector spaces over a field F, and let spanU = {u₁, ..., u_n}. Suppose further that X: U->V and Y: V->U are linear transformations such that Xu_i= Yu_ifor i = 1, ..., n. Prove X = Y

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