## College Algebra (10th Edition)

Published by Pearson

# Chapter 8 - Section 8.2 - Systems of Linear Equations: Matrices - 8.2 Assess Your Understanding - Page 571: 33

#### Answer

$\left\{\begin{array}{lllll} x_{1} & & & & =1\\ & x_{2} & & +x_{4} & =2\\ & & x_{3} & +2x_{4} & =3 \end{array}\right.$ The system is consistent. Solution set = $\{(x_{1},x_{2},x_{3},x_{4})\ |\ x_{1}=1,\ \ x_{2}=2-x_{4}\ x_{3}=3-2x_{4},\ x_{4} \in \mathbb{R} \}$

#### Work Step by Step

The system represented by the augmented matrix is $\left\{\begin{array}{lllll} x_{1} & & & & =1\\ & x_{2} & & +x_{4} & =2\\ & & x_{3} & +2x_{4} & =3 \end{array}\right.$ The system is consistent. Take $x_{4}\in \mathbb{R}$, Equation 3 $\Rightarrow x_{3}=3-2x_{4}$ Equation 2 $\Rightarrow x_{2}=2-x_{4}$ Equation 1 $\Rightarrow x=1$ Solution set = $\{(x_{1},x_{2},x_{3},x_{4})\ |\ x_{1}=1,\ \ x_{2}=2-x_{4}\ x_{3}=3-2x_{4},\ x_{4} \in \mathbb{R} \}$

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