I am currently trying to show that the Row space of $V$ is the orthogonal complement of the Null space of $V$. That is:
$R(V) = N(V)^\perp$.
This seems like a straight-forward proof and my strategy is to prove that $R(V) \subset N(V)^\perp$ and that $N(V)^\perp \subset R(V)$. I think I have the first down, but am not sure how I would approach the second. Would anyone have any ideas? Thank you!