Answer
The answer is $\left[\begin{array}{cc|c}
1 & -\frac{2}{5} & \frac{3}{4} \\
0 &\frac{18}{5} &-4 \\
\end{array}\right]$.
Work Step by Step
The given matrix is
$\left[\begin{array}{cc|c}
1 & -\frac{2}{5} & \frac{3}{4} \\
4 &2 &-1 \\
\end{array}\right]$
Perform $ -4R_1+R_2 $.
Multiply row 1 by $ -4$ and add to the row 2 as shown below.
$\left[\begin{array}{cc|c}
1 & -\frac{2}{5} & \frac{3}{4} \\
-4\cdot 1+4 &-4\cdot (-\frac{2}{5})+ 2 &-4\cdot ( \frac{3}{4} )-1 \\
\end{array}\right]$
Simplify.
$\left[\begin{array}{cc|c}
1 & -\frac{2}{5} & \frac{3}{4} \\
-4+4 &\frac{8}{5} +2 &-3-1 \\
\end{array}\right]$
$\left[\begin{array}{cc|c}
1 & -\frac{2}{5} & \frac{3}{4} \\
0 &\frac{8+10}{5} &-4 \\
\end{array}\right]$
$\left[\begin{array}{cc|c}
1 & -\frac{2}{5} & \frac{3}{4} \\
0 &\frac{18}{5} &-4 \\
\end{array}\right]$.
