Question: Problem 2 Let V and W be two finite-dimensional vector spaces, and B (resp. v) be an ordered basis of V (resp. W). Let T:

Problem 2 Let V and W be two finite-dimensional vector spaces, and B (resp. v) be an ordered basis of V (resp. W). Let T: V - W be a linear transformation. Prove that if T is an isomorphism, then is an invertible matrix. (You can find the proof in Section 2.4 of the textbook, but the point is that you should be able to reproduce the proof without much effort.) Optional slightly more challenging problem: Prove the converse statement. Namely, if g is an invertible matrix, then T is an isomorphism. Proof. 0

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