Problem in Linear Algebra about dimension of vector space Let U and V be finite dimensional vector spaces Over $\mathbb R$, Let $L(U,V)$ be the vector space of linear transformations from $U$ to $V$, and Let $W$ be a vector subspace of $U$.  
If $Z$= {$T$ $\in L(U,V)$: $T(w)=0$ for all w $\in  W$}, then What is the vector space dimension Dim($Z$) of $Z$ in terms of vector space dimension of $U$, $V$, and $W$?
I have no idea how to start about this problem?

Hint: Choose a basis of $W$ and extend it to a basis of $U$.
Express $T$ in that basis as a matrix.
How many degrees of freedom are left?
