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Consider vector spaces with scalars in the field F(could be R or C). Recall that L(V,...

Consider vector spaces with scalars in the field F(could be R or C). Recall that L(V, W) is the vectors space consisting of all linear transformations from V to W.

a. Prove that L(F, W) is isomorphic to W.

b. Assume that V is a finite dimensional vectors space. Prove that L(V, F) is isomorphic to V.

c. If V is infinite dimensional, what happens to L(V, F)?

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