Answer
$(3,1,2)$
Work Step by Step
Write the augmented matrix and,
using row transformations,
arrive at the row-reduced echelon form.
$\left[\begin{array}{llll}
0 & 2 & 1 & 4\\
1 & 1 & 0 & 4\\
3 & 3 & -1 & 10
\end{array}\right]$
Swap rows 1 and 2,
$\left[\begin{array}{llll}
1 & 1 & 0 & 4\\
0 & 2 & 1 & 4\\
3 & 3 & -1 & 10
\end{array}\right] \ \ \begin{array}{l}
.\\
.\\
R_{3}-3R_{1}\rightarrow R_{3}.
\end{array}$
$\left[\begin{array}{llll}
1 & 1 & 0 & 4\\
0 & 2 & 1 & 4\\
0 & 0 & -1 & -2
\end{array}\right] \ \ \begin{array}{l}
.\\
+R_{3}.\\
\times(-1).
\end{array}$
$\left[\begin{array}{llll}
1 & 1 & 0 & 4\\
0 & 2 & 0 & 2\\
0 & 0 & 1 & 2
\end{array}\right]\ \ \begin{array}{l}
.\\
\div 2.\\
.
\end{array}$
$\left[\begin{array}{llll}
1 & 1 & 0 & 4\\
0 & 1 & 0 & 1\\
0 & 0 & 1 & 2
\end{array}\right]\ \ \begin{array}{l}
-R_{2}.\\
.\\
.
\end{array}$
$\left[\begin{array}{llll}
1 & 0 & 0 & 3\\
0 & 1 & 0 & 1\\
0 & 0 & 1 & 2
\end{array}\right]$
Solution: $(3,1,2)$
