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: 32

Answer

$(-3,-2,-3)$

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 $T(-2,1,0)=2T(1,1,1)+T(0,-1,2)-4T(1,0,1)=2(2,0,-1)+(-3,2,-1)-4(1,1,0)=(4,0,-2)+(-3,2,-1)+(-4,-4,0)=(-3,-2,-3)$
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