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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- May 10th 2010, 12:32 AMquesFinite Dimensional Vector Space
**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 - May 10th 2010, 11:06 AMNonCommAlg