Answer
Row Echelon Form:
$$
\begin{bmatrix}
1 & 1 & 1 \\
0 & 1 & 1 \\
0 & 0 & 1 \\
\end{bmatrix}
$$
Reduced Row Echelon Form:
$$
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1 \\
\end{bmatrix}
$$
Work Step by Step
We're given
$$
\begin{bmatrix}
0 & 0 & 1 \\
0 & 1 & 1 \\
1 & 1 & 1 \\
\end{bmatrix}
$$
First, swap rows 1 and 3, to get the row echelon form:
$$
\begin{bmatrix}
1 & 1 & 1 \\
0 & 1 & 1 \\
0 & 0 & 1 \\
\end{bmatrix}
$$
Now, subtract row 3 from rows 1 and 2:
$$
\begin{bmatrix}
1 & 1 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1 \\
\end{bmatrix}
$$
And subtract row 2 from row 1:
$$
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1 \\
\end{bmatrix}
$$
The matrix is now in reduced row echelon form.
