Dimension of nullspace and number of rows 
A matrix $A$ has $10$ columns and dim(Null($A^{T}$ ))$=7$. The smallest possible number of rows of $A$ is
$(A)$ $5$
$(B)$ $6$
$(C)$ $7$
$(D)$ $8$
$(E)$ $9$

I know that dim(Null($A^{T}$ ))$=7$ implies that there are $7$ rows of zeros and that:
Rank($A$)+Nullity($A^T$) $=$ # of rows
Rank($A$)+Nullity($A$) $=$ # of columns
I'm not really sure how to use all this information though... Can someone provide a hint?

$A$ has $10$ columns implies you can view $A$ as a linear map $A:\Bbb R^{10} \to \Bbb R^m$ and $A^T$ as a linear map $A^T:\Bbb R^{m} \to \Bbb R^{10}$ where the $m$ we do not know. Here $\dim (\text{Null}( A^T))=7$ implies $7 \leq m$  and $\text{rank}(A^T) \le 10$. Also $\text{rank}(A^T)=\text{rank}(A) \leq m$. so $7 \leq m \leq 10$
