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?

Hint: You want Rank($A$)+Nullity($A^T$) to be as low as possible. You already know how large the right term is. What's the lowest possible the left term could theoretically be? What would the resulting matrix be?
