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: 17

Answer

$$x=3a$$

Work Step by Step

We're given $$x-a=2(x-2a)$$ Distributing scalar multiplication over vector addition on the right hand side, we get: $$x-a=2x-4a$$ By subtracting $2x-a$ from both sides, we then move all the $x$s to the left side and all the $a$s to the right: $$-x=-3a$$ Lastly, dividing both sides by $-1$ yields $$x=3a$$
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