Answer
$\left[\begin{array}{llllll}
1 & -1 & 1 & 1 & | & 3\\
0 & 1 & -2 & -1 & | & 0\\
0 & 2 & 1 & 2 & | & 5\\
0 & 6 & -3 & -1 & | & -9
\end{array}\right]$
Work Step by Step
The elements of the third row will be replaced with
$-2(1)+2=0,$
$-2(-1)+0=2,$
$-2(1)+3=1,$
$-2(1)+4=2,$
$-2(3)+11=5$, to become
$0\ \ 2\ \ 1\ \ 2\ \ |\ \ 5.$
The elements of the fourth row will be replaced with
$-5(1)+5=0,$
$-5(-1)+1=6,$
$-5(1)+2=-3,$
$-5(1)+4=-1,$
$-5(5)+6=-9$, to become
$0\ \ 6\ \ -3\ \ -1\ \ |\ \ -9$
so, the resulting matrix is
.
$\left[\begin{array}{llllll}
1 & -1 & 1 & 1 & | & 3\\
0 & 1 & -2 & -1 & | & 0\\
0 & 2 & 1 & 2 & | & 5\\
0 & 6 & -3 & -1 & | & -9
\end{array}\right]$
