Which number in the array below is both the largest in its column and the smallest in its row?  (Columns go up and down, rows go right and left.)
\[\begin{tabular}[t]{ccccc} 10 & 6 & 4 & 3 & 2 \\ 11 & 7 & 14 & 10 & 8 \\ 8 & 3 & 4 & 5 & 9 \\ 13 & 4 & 15 & 12 & 1 \\ 8 & 2 & 5 & 9 & 3 \end{tabular}\]
$\text{(A)}\ 1 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 7 \qquad \text{(D)}\ 12 \qquad \text{(E)}\ 15$
The largest numbers in the first, second, third, fourth and fifth columns are $13,7,15,12,9$ respectively.  Of these, only $7$ is the smallest in its row $\rightarrow \boxed{\text{C}}$.