Thread: Finite 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

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