## In which $\R^k$, are the Nullspace and Range Subspaces?

## Problem 712

Let $A$ be an $m \times n$ matrix.

Suppose that the nullspace of $A$ is a plane in $\R^3$ and the range is spanned by a nonzero vector $\mathbf{v}$ in $\R^5$. Determine $m$ and $n$. Also, find the rank and nullity of $A$.