REF
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A matrix is in 2.1 REF if
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rows with all zero entries (zero rows) if any are all below all non-zero rows
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for any two non-zero rows, the first non-zero entry (leading entry) in the upper row is to the left of the leading entry in the lower rows
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Examples
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solve the following system by converting to REF$$ \begin{align} x+y=5 \
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x+z=7 \
y+z=5
\end{align}
\begin{bmatrix}
1 & 1 & 0 & |5 \
1 & 0 & 1 & |7 \
0 & 1 & 1 & |5
\end{bmatrix}R_{2}-R_{1},R_{3}+R_{2}\implies\begin{bmatrix}
1 & 1 & 0 & |5 \
0 & -1 & 1 & |2 \
0 & 0 & 2 & |7
\end{bmatrix}(REF)
\begin{align} x+y=5\implies x=\frac{7}{2} \
y-z=-2\implies y=\frac{3}{2} \
z=\frac{7}{2}
\end{align}