Answer
The system is inconsistent.
Work Step by Step
5$x_{1}$ - 3$x_{2}$ + 2$x_{3}$ = 3
4$x_{1}$ + 2$x_{2}$ - $x_{3}$ = 7
$x_{1}$ - 11$x_{2}$ + 4$x_{3}$ = 3
$R_{1}$↔$R_{3}$
$x_{1}$ - 11$x_{2}$ + 4$x_{3}$ = 3
4$x_{1}$ + 2$x_{2}$ - $x_{3}$ = 7
5$x_{1}$ - 3$x_{2}$ + 2$x_{3}$ = 3
-2$R_{1}$+$R_{2}$→$R_{2}$
-5$R_{1}$+$R_{3}$→$R_{3}$
$x_{1}$ - 11$x_{2}$ + 4$x_{3}$ = 3
26$x_{2}$ - 9$x_{3}$ = 1
52$x_{2}$ - 18$x_{3}$ = -12
-2$R_{2}$+$R_{3}$→$R_{3}$
$x_{1}$ - 11$x_{2}$ + 4$x_{3}$ = 3
26$x_{2}$ - 9$x_{3}$ = 1
0 = -14
0 $\ne$ -14, so the system has no solution.
