Answer
The answer is $\left[\begin{array}{cc|c}
1 & -3 & 1 \\
0 &7 &-7 \\
\end{array}\right]$.
Work Step by Step
The given matrix is
$\left[\begin{array}{cc|c}
1 & -3 & 1 \\
2 & 1 &-5 \\
\end{array}\right]$.
Perform $ -2R_1+R_2 $.
Multiply row 1 with $-2 $ and add to the row 2 as shown below.
$\left[\begin{array}{cc|c}
1 & -3 & 1 \\
-2\cdot 1+2 &-2\cdot(-3)+ 1 &-2\cdot 1-5 \\
\end{array}\right]$
Simplify.
$\left[\begin{array}{cc|c}
1 & -3 & 1 \\
-2+2 &+6+ 1 &-2-5 \\
\end{array}\right]$
$\left[\begin{array}{cc|c}
1 & -3 & 1 \\
0 &7 &-7 \\
\end{array}\right]$.
