Was this the complete statement of the problem? It doesn't quite make sense. You specify that V is a "vector space over F" but say nothing about W. Further, the range of T is a subspace of W while null(T) is a subspace of V. Are you assuming that V and W are the same? If not what do you mean by the "intersection" of two subspace ofdifferentvector spaces?

Assuming that V= W, suppose v is in "null(T)". What does that tell you about v? Suppose w is in range(T). What does that tell you about w?