Let V be the real vector space of all real 2x3 matrices, and let W be the real vector space of all real 4x1 column vectors. If T is a linear transformation from V onto W, what is the dimension of the subspace {vV: T(v) =0}?

ker(v)=nullity; therefore, the range ofv=6.

I know the answer is 2 but how do I show it?