Answer
See answer below
Work Step by Step
a) We obtain $\begin{bmatrix}
1 & 1 & -3 & 2\\
3 & 4 & -11 & 7
\end{bmatrix} \approx
\begin{bmatrix}
1 & 1 & -3 & 2\\
0 & 1 & -2 & 1
\end{bmatrix}$
Since $n=4$, the basis for the row-space is of $A$ spanned by the given factors is $\{(1,1,-3,2);(0,1,-2,1)\}$.
b) We notice that the first and second columns of $A$ are dependent. So, the basis for column-space of $A$ is equal to $\{(1,3),(1,4)\}$ with $m=2$.
