Answer
Row Echelon Form:
$$
\begin{bmatrix}
2 && -4 && -2 && 6 \\
0 && 7 && 9 && -3 \\
\end{bmatrix}$$
Reduced Row Echelon Form:
$$
\begin{bmatrix}
1 && 0 && \frac{11}{7} && \frac{15}{7} \\
0 && 1 && \frac{9}{7} && -\frac{3}{7} \\
\end{bmatrix}$$
Work Step by Step
$$
\begin{bmatrix}
2 && -4 && -2 && 6 \\
3 && 1 && 6 && 6 \\
\end{bmatrix}$$
Subtract $\frac{3}{2}$ times row 1 from row 2
$$\sim
\begin{bmatrix}
2 && -4 && -2 && 6 \\
0 && 7 && 9 && -3 \\
\end{bmatrix}$$
Which is in row echelon form
Divide row 1 by 2
$$\sim
\begin{bmatrix}
1 && -2 && -1 && 3 \\
0 && 7 && 9 && -3 \\
\end{bmatrix}$$
Divide row 2 by 7
$$\sim
\begin{bmatrix}
1 && -2 && -1 && 3 \\
0 && 1 && \frac{9}{7} && -\frac{3}{7} \\
\end{bmatrix}$$
Add 2 times row 2 to row 1
$$\sim
\begin{bmatrix}
1 && 0 && \frac{11}{7} && \frac{15}{7} \\
0 && 1 && \frac{9}{7} && -\frac{3}{7} \\
\end{bmatrix}$$
Which is in Reduced Row Echelon Form
