Answer
Row Echelon Form:
$$
\begin{bmatrix}
3 && 5 \\
0 && -\frac{31}{3} \\
0 && 0
\end{bmatrix}$$
Reduced Row echelon form:
$$
\begin{bmatrix}
1 && 0 \\
0 && 1 \\
0 && 0
\end{bmatrix}$$
Work Step by Step
$$
\begin{bmatrix}
3 && 5 \\
5 && -2 \\
2 && 4
\end{bmatrix}$$
Subtract $\frac{5}{3}$ times row 1 from row 2 &
Subtract $\frac{2}{3}$ times row 1 from row 3
$$\sim
\begin{bmatrix}
3 && 5 \\
0 && -\frac{31}{3} \\
0 && \frac{2}{3}
\end{bmatrix}$$
Add $\frac{2}{31}$ times row 2 to row 3
$$\sim
\begin{bmatrix}
3 && 5 \\
0 && -\frac{31}{3} \\
0 && 0
\end{bmatrix}$$
Which is in row echelon form
Divide row 1 by 3
$$\sim
\begin{bmatrix}
1 && \frac{5}{3} \\
0 && -\frac{31}{3} \\
0 && 0
\end{bmatrix}$$
Multiply row 2 by -(3/31)
$$\sim
\begin{bmatrix}
1 && \frac{5}{3} \\
0 && 1 \\
0 && 0
\end{bmatrix}$$
Subtract $\frac{5}{3}$ times row 2 from row 1
$$\sim
\begin{bmatrix}
1 && 0 \\
0 && 1 \\
0 && 0
\end{bmatrix}$$
Which is in reduced row echelon form.
