Answer
See answers below
Work Step by Step
a) We obtain $\begin{bmatrix}
1 & -1 & 2 & 3\\
1 & 1 & -2 & 6\\
3 & 1 & 4 & 2
\end{bmatrix}\approx \begin{bmatrix}
1 & -1 & 2 & 3\\
0 & 2 & -4 & 3\\
0 & 4 & -2 & -7
\end{bmatrix} \approx \begin{bmatrix}
1 & -1 & 2 & 3\\
0 & 2 & -4 & 3\\
0 & 0 & 6 & -13
\end{bmatrix} \approx \begin{bmatrix}
1 & -1 & 2 & 3\\
0 & 1 & -2 & \frac{3}{2}\\
0 & 0 & 1 & -\frac{13}{6}
\end{bmatrix} $
Since $n=4$, the basic for row space $A$ is $\{(1,-1,2,3);(0,2,-4,3);(0,0,6,-13)\}$
b) We notice that the first, second and third columns are independent. Since $m=3$ the basic for colspace $A$ is $\{1,1,3);(-1,1,1);(2,-2,4)\}$
