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QUESTION
Let V and W be finite-dimensional vector spaces and let S:V W and T :W V be linear maps such that TS = idV .
1. Let V and W be finite-dimensional vector spaces and let S:V →W and T :W →V be linear maps such that TS = idV .(a) Express the dimensions of the null spaces and ranges of S and T in terms of dimensions of V and W .(b) Which values dim V and dim W can take in this situation?
