## Elementary Linear Algebra 7th Edition

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.