Let V, W be finite dimensional vector spaces over a field k and let Z subset of W be a subspace. Let T : V -> W be a linear map. Prove that dim( T^(-1) ( Z ) ) <= dim V - dim W + dim Z
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Originally Posted by ques Let V, W be finite dimensional vector spaces over a field k and let Z subset of W be a subspace. Let T : V -> W be a linear map. Prove that dim( T^(-1) ( Z ) ) <= dim V - dim W + dim Z your inequality is not correct. it should be instead of let and define the map by clearly and thus hence therefore
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