Answer
The system is inconsistent
Work Step by Step
3$x_{1}$ + 2$x_{2}$ + 4$x_{3}$ = 1
$x_{1}$ + $x_{2}$ - 2$x_{3}$ = 3
2$x_{1}$ - 3$x_{2}$ + 6$x_{3}$ = 8
$R_{1}$↔$R_{2}$
$x_{1}$ + $x_{2}$ - 2$x_{3}$ = 3
3$x_{1}$ + 2$x_{2}$ + 4$x_{3}$ = 1
2$x_{1}$ - 3$x_{2}$ + 6$x_{3}$ = 8
-3$R_{1}$+$R_{2}$→$R_{2}$
-2$R_{1}$+$R_{1}$→$R_{1}$
$x_{1}$ + $x_{2}$ - 2$x_{3}$ = 3
-5$x_{2}$ + 10$x_{3}$ = -8
-5$x_{2}$ + 10$x_{3}$ = 2
-$R_{2}$+$R_{3}$→$R_{3}$
$x_{1}$ + $x_{2}$ - 2$x_{3}$ = 3
-5$x_{2}$ + 10$x_{3}$ = -8
0 = 10
0$\ne$10, so the system has no solution.
