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: 12

Answer

$$[6,9,-1]$$

Work Step by Step

Compute the resultant vector $x = 3b - 2c + d$ by computing each of its components. Note that $x_n = 3b_n - 2c_n + d_n$, so for each component we have: $$x_1 = 3b_1 - 2c_1 + d_1 = 3(3) - 2(1)-1=6$$ $$x_2 = 3b_2 - 2c_2 + d_2 = 3(2) -2(-2)-1=9$$ $$x_3 = 3b_3 - 2c_3 + d_3 = 3(1) -2(1)-2=-1$$ Thus, $x = [x_1, x_2, x_3] = [6, 9, -1]$
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