Problem 3. Suppose L: V W is a linear transformation from a vector space V into a vector space W. The preimage of a subspace of W is the set of all vectors in V whose images are in the subspace. That is, if U CW is a subspace of W, then the preimage is defined as L-(U) := {T e V such that L(7) E U}. Prove that L-1(U) is a vector subspace of V.

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