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: 31

Answer

$(2,2.5,2)$

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 $T(2,-1,1)=-1.5T(1,1,1)-0.5T(0,-1,2)+3.5T(1,0,1)=-1.5(2,0,-1)-0.5(-3,2,-1)+3.5(1,1,0)=(-3,0,1.5)+(1.5,-1,0.5)+(3.5,3.5,0)=(2,2.5,2)$
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