Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 1 - Systems of Linear Equations - 1.1 Introduction to Systems of Linear Equations - 1.1 Exercises: 48

Answer

$x$ = 0, $y$ = 4, $z$ =-2

Work Step by Step

$x$ + $y$ + $z$ = 2 -$x$ + 3$y$ + 2$z$ = 8 4$x$ + $y$ = 4 $R_{1}$+$R_{2}$→$R_{2}$ $x$ + $y$ + $z$ = 2 4$y$ + 3$z$ = 10 4$x$ + $y$ = 4 -4$R_{1}$+$R_{3}$→$R_{3}$ $x$ + $y$ + $z$ = 2 4$y$ + 3$z$ = 10 -3$y$ - 4$z$ = -4 3$R_{2}$→$R_{2}$ 4$R_{3}$→$R_{3}$ $x$ + $y$ + $z$ = 2 12$y$ + 9$z$ = 30 -12$y$ - 16$z$ = -16 $R_{2}$+$R_{3}$→$R_{3}$ $x$ + $y$ + $z$ = 2 12$y$ + 9$z$ = 30 -7$z$ = -14 $z$ = -2, plug this value into (12$y$ + 9$z$ = 30) 12$y$ + 9(-2) = 30 $y$ = 4 $x$ + (4) + (-2) = 2 $x$ = 0
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