<s>[INST] Find Matrix $B$ s.t $Rowspan(A)=Rowspan(B)$ And $(1,1,1)\in Columnspan(B)$ 
Let $A=\begin{pmatrix} 
1 & 0 & 3 \\
2 & 1 & 5 \\
-1 & 2 &-5 
\end{pmatrix}$ 
Find a matrix $B$ such that $Rowspan(A)=Rowspan(B)$ and $\begin{pmatrix} 
1  \\
1  \\
1 
\end{pmatrix}\in Columnspan(B)$

So to find $Rowspan(A)$ I row reduced $\begin{pmatrix} 
1 & 0 & 3 \\
2 & 1 & 5 \\
-1 & 2 &-5 
\end{pmatrix}$ to  $\begin{pmatrix} 
1 & 0 & 3 \\
0 & 1 & -1 \\
0 & 0 &0 
\end{pmatrix}$ and because row operations do not change the row span so $B$ should span the same space of $CF(A)$ and  $\begin{pmatrix} 
1  \\
1  \\
1 
\end{pmatrix}\in Columnspan(B)$
But where should I start?
 [/INST] From here
$$A^{RREF}=\begin{pmatrix} 
1 & 0 & 3 \\
0 & 1 & -1 \\
0 & 0 &0 
\end{pmatrix}$$
you are done, indeed just consider
$$B=\begin{pmatrix} 
1 & 0 & 3 \\
0 & 1 & -1 \\
1 & 0 &3 
\end{pmatrix}$$
and note that $$B\cdot (1,1,0)=(1,1,1)$$
</s>