Answer
(4,4,4)
Work Step by Step
Write the augmented matrix and,
using row transformations arrive at the reduced row echelon form.
-----------
$\left[\begin{array}{llll}
-1 & 2 & -1 & 0\\
-1 & -1 & 2 & 0\\
2 & 0 & -1 & 4
\end{array}\right]\begin{array}{l}
\times(-1).\\
-R_{1}.\\
+2R_{1}.
\end{array}$
... leading 1 in row 1,
... clear column 1,
$\left[\begin{array}{llll}
1 & -2 & 1 & 0\\
0 & -3 & 3 & 0\\
0 & 2 & -1 & 4
\end{array}\right]\begin{array}{l}
.\\
\div(-3).\\
.
\end{array}$
... leading 1 in row 2,
$\left[\begin{array}{llll}
1 & -2 & 1 & 0\\
0 & 1 & -1 & 0\\
0 & 2 & -1 & 4
\end{array}\right]\begin{array}{l}
+2R_{2}.\\
.\\
-2R_{2}.
\end{array}$
... clear column 2,
$\left[\begin{array}{llll}
1 & 0 & -1 & 0\\
0 & 1 & -1 & 0\\
0 & 0 & 1 & 4
\end{array}\right]\begin{array}{l}
+R_{3}.\\
+R_{3}.\\
.
\end{array}$
... clear column 3,
$\left[\begin{array}{llll}
1 & 0 & 0 & 4\\
0 & 1 & 0 & 4\\
0 & 0 & 1 & 4
\end{array}\right]$
Solution: (4,4,4)
