I think I have this one figured out, but I'm not exactly sure... maybe somebody can clarify things a bit for me.

The problem is: Let V be the vector space consisting of all real 2x3 matrices and W be the vector space consisting of all 4x1 matrices. If T is a linear transformation from V onto W, what is the dimension of the subspace {v in V, such that T(v) = 0}.

This is of course the kernel of T. The rank nullity theorem gives that Dim(Ker(T))+Dim(Im(T)) = Dim(V). Since Dim(Im(T)) = Dim(W) = 4x1 = 4 and Dim(V) = 2x3 = 6, we have that Dim(Ker(T)) = Dim(V)-Dim(W) = 6 - 4 = 2... right?

Peter