# Chapter 1 - Systems of Linear Equations - 1.1 Introduction to Systems of Linear Equations - 1.1 Exercises - Page 10: 50

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.

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