Chapter 4.8, Problem 8P

For Problem $3-9$, (a) find $n$ such that $\text{rowspace}\left(A\right)$ is a subspace of ${ℝ}^n$, and determine a basis for $\text{rowspace}\left(A\right)$; (b) find $m$ such that $\text{colspace}\left(A\right)$ is a subspace of ${ℝ}^m$, and determine a basis for $\text{colspace}\left(A\right)$.

$A=\left[\begin{array}{cccc}1& 2& -1& 3\\ 3& 6& -3& 5\\ 1& 2& -1& -1\\ 5& 10& -5& 7\end{array}\right]$.