You shoould explain stuff better so that people won't to guess what you meant: here V is a vector spcae over field F and T V --> F is a linear trasf., or much better and more widely knows as linear functional. Then...etc.

Well, this is simple: if dim_F (V) = n and since dim_F (F) = 1 , use now the well-known dimensions theorem for linear transformations between finite dimensional vector spaces.

Tonio