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 {v$\displaystyle \in$ V: T(v) =0}?

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

$\displaystyle \begin{bmatrix}

a & b & c\\

d & e & f

\end{bmatrix}$

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