Linear Algebra: A Modern Introduction

Published by Cengage Learning
ISBN 10: 1285463242
ISBN 13: 978-1-28546-324-7

Chapter 1 - Vectors - 1.1 The Geometry and Algebra of Vectors - Exercises 1.1: 18

Answer

$$x=1.5a-1.5b$$

Work Step by Step

We're given: $$x+2a-b=3(x+a)-2(2a-b)$$ First, distribute the scalar-vector multiplications on the right hand side: $$x+2a-b=3x+3a-4a+2b$$ Next, add up the $a$ terms on the right: $$x+2a-b=3x-a+2b$$ Subtract $3x$ from both sides to move all the $x$ terms to the left: $$-2x+2a-b=-a+2b$$ Now subtract $2a-b$ from both sides to move all the $a$ and $b$ terms to the right: $$-2x=-3a+3b$$ Lastly, divide both sides by $-2$, leaving us with: $$x=1.5a-1.5b$$
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