Answer
$\left[\begin{array}{lllll}
1 & -1 & 1/2 & | & -1/2\\
1 & 2 & -1 & | & 2\\
6 & 4 & 3 & | & 5
\end{array}\right]$
Work Step by Step
The elements of the third row will be replaced with
$2\displaystyle \rightarrow\quad\frac{1}{2}\cdot 2=1$
$-2\displaystyle \rightarrow\quad\frac{1}{2}\cdot(-2)=-1 $
$1\displaystyle \rightarrow\quad\frac{1}{2}\cdot(1)=\frac{1}{2}$
$-1\displaystyle \rightarrow\quad\frac{1}{2}\cdot(-1)=-\frac{1}{2}$
so the new matrix is
$\left[\begin{array}{lllll}
1 & -1 & 1/2 & | & -1/2\\
1 & 2 & -1 & | & 2\\
6 & 4 & 3 & | & 5
\end{array}\right]$
