I have two vector spaces, $A$ and $B$, and one subspace from each, $U$ and $W$, respectively. How can I prove these subspaces are equal?
If it matters, in this case $A$ is a matrix with components in $\mathbb{R}$. Taking each row as a vector, $U$ is a subspace from $\mathbb{R}^n$ generated by these vectors. Then I have $B$, which is RREF of $A$, and I take each of its rows as vectors and $W$ is the subspace generated by these vectors.
Also, how can I prove the vectors obtained from non-null rows of $B$ are linearly independent?
