Question: 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

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

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