Answer
See answers below
Work Step by Step
a) We obtain $\begin{bmatrix}
1 & 2 & -1 & 3\\
3 & 6 & -3 & 5\\
1 & 2 & -1 & -1 \\
5 & 10 & -5 & 7
\end{bmatrix}\approx \begin{bmatrix}
1 & 2 & -1 & 3\\
0 & 0 & 0 & -4\\
0 & 0 &0 & -4 \\
0 & 0 & 0 & 8
\end{bmatrix} \approx \begin{bmatrix}
1 & 2 & -1 & 3\\
0 & 0 & 0 & -4\\
0 & 0 &0 & 0 \\
0 & 0 & 0 & 0
\end{bmatrix} \approx\begin{bmatrix}
1 & 2 & -1 & 3\\
0 & 0 & 0 & 1\\
0 & 0 &0 & 0 \\
0 & 0 & 0 & 0
\end{bmatrix} $
Since $n=4$, the basic for row space $A$ is $\{(1,2,-1,3);(0,0,0,1)\}$
b) We notice that the second column is independent. Since $m=4$ the basic for colspace $A$ is $\{1,3,1,5);((3,5,1,-7)\}$
