Answer
See answer below
Work Step by Step
a) We obtain $\begin{bmatrix}
1 & 2 & 3\\
5 & 6 & 7\\
9 & 10 & 11
\end{bmatrix}\approx\begin{bmatrix}
1 & 2 & 3\\
0 & -4 & -8\\
0 & -8 & 16
\end{bmatrix} \approx \begin{bmatrix}
1 & 2 & 3\\
0 & -4 & -8\\
0 & 0 & 0
\end{bmatrix} \approx \begin{bmatrix}
1 & 2 & 3\\
0& 1 &2\\
0 & 0 & 0
\end{bmatrix}$
Since $n=3$, the basic for row space $A$ is $\{(1,2,3);(0,1,2)\}$
b) We notice that the first and second columns are independent. Hence, the basic for colspace $A$ is $\{1,5,9);(2,6,10)\}$
