Answer
The answer is $\left[\begin{array}{cc|c}
1 & -\frac{3}{2} & \frac{7}{2} \\
0 &\frac{17}{2} &\frac{-17}{2} \\
\end{array}\right]$.
Work Step by Step
The given matrix is
$\left[\begin{array}{cc|c}
1 & -\frac{3}{2} & \frac{7}{2} \\
3 &4 &2 \\
\end{array}\right]$
Perform $ -3R_1+R_2 $.
Multiply row 1 by $-3$ and add to the row 2 as shown below.
$\left[\begin{array}{cc|c}
1 & -\frac{3}{2} & \frac{7}{2} \\
-3\cdot 1+3 &-3\cdot (-\frac{3}{2})+4 &-3\cdot (\frac{7}{2})+2 \\
\end{array}\right]$
Simplify.
$\left[\begin{array}{cc|c}
1 & -\frac{3}{2} & \frac{7}{2} \\
-3+3 &\frac{9}{2}+4 &-\frac{21}{2}+2 \\
\end{array}\right]$
$\left[\begin{array}{cc|c}
1 & -\frac{3}{2} & \frac{7}{2} \\
0 &\frac{9+8}{2} &\frac{-21+4}{2} \\
\end{array}\right]$
$\left[\begin{array}{cc|c}
1 & -\frac{3}{2} & \frac{7}{2} \\
0 &\frac{17}{2} &\frac{-17}{2} \\
\end{array}\right]$.
