Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 8 - Review Exercises - Page 617: 41


(a) $u+v=⟨-4,3⟩$ (b) $u-v=⟨2,-9⟩$ (c) $4u=⟨-4,-12⟩$ (d) $3v+5u=⟨-14,3⟩$

Work Step by Step

(a) $u+v=⟨-1,-3⟩+⟨-3,6⟩=⟨-1+(-3),-3+6⟩=⟨-1-3,3⟩=⟨-4,3⟩$ (b) $u-v=⟨-1,-3⟩-⟨-3,6⟩=⟨-1-(-3),-3-6⟩=⟨-1+3,-9⟩=⟨2,-9⟩$ (c) $4u=4⟨-1,-3⟩=⟨4(-1),4(-3)⟩=⟨-4,-12⟩$ (d) $3v+5u=3⟨-3,6⟩+5⟨-1,-3⟩=⟨3(-3),3(6)⟩+⟨5(-1),5(-3)⟩=⟨-9,18⟩+⟨-5,-15⟩=⟨-9+(-5),18+(-15)⟩=⟨-9-5,18-15⟩=⟨-14,3⟩$
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