Answer
the reduced echelon form is
$$\left[ \begin {array}{ccc} 1&0 &-1\\ 0&1&2
\\ 0&0&0\end {array} \right].
$$
Work Step by Step
Given the matrix $$\left[ \begin {array}{ccc} 1&2&3\\ 4&5&6
\\ 7&8&9\end {array} \right]
$$
Multiply the first row by $-4$ and adding it to the second row, we get
$$\left[ \begin {array}{ccc} 1&2&3\\ 0&-3&-6
\\ 0&-6&-12\end {array} \right]
$$
Multiply the second row by $-2$ and adding it to the third row, we have
$$\left[ \begin {array}{ccc} 1&2&3\\ 0&-3&-6
\\ 0&0&0\end {array} \right]
$$
Multiply the second row by $-\frac{1}{3}$, we have
$$\left[ \begin {array}{ccc} 1&2&3\\ 0&1&2
\\ 0&0&0\end {array} \right]
$$
Multiply the second row by $-2$ and adding it to the first row, we get the reduced echelon form
$$\left[ \begin {array}{ccc} 1&0&-1\\ 0&1&2
\\ 0&0&0\end {array} \right].
$$
