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: 29

Answer

$(5,0,1)$

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 $T(2,1,0)=-T(0,-1,2)+2T(1,0,1)=-(-3,2,-1)+2(1,1,0)=(3,-2,1)+(2,2,0)=(5,0,1)$
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