Elementary Linear Algebra 7th Edition

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

Chapter 6 - Linear Transformations - 6.1 Introduction to Linear Transformations - 6.1 Exercises - Page 300: 27

Answer

$(0,-6,8)$

Work Step by Step

In this case the transformation is linear if $T(v_1+v_2)=T(v_1)+T(v_2)$ and $T(av_1)=aT(v_1)$ for any $v_1,v_2$ in the domain and any $a$ scalar. Hence $T(2,-4,1)=2T(1,0,0)-4T(0,1,0)+T(0,0,1)=2(2,4,-1)-4(1,3,-2)+(0,-2,2)=(4,8,-2)-(4,12,-8)+(0,-2,2)=(0,-6,8)$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.

GradeSaver will pay $15 for your literature essays
GradeSaver will pay $25 for your college application essays
GradeSaver will pay $50 for your graduate school essays – Law, Business, or Medical
GradeSaver will pay $10 for your Community Note contributions
GradeSaver will pay $500 for your Textbook Answer contributions