Differential Equations and Linear Algebra (4th Edition)

by Goode, Stephen W.; Annin, Scott A.

Published by Pearson

ISBN 10: 0-32196-467-5

ISBN 13: 978-0-32196-467-0

Chapter 6 - Linear Transformations - 6.1 Definition of a Linear Transformation - Problems - Page 390: 32

Answer

$T(v_1)=8v_1-4v_2\\ T(v_2)=-5v_1+3v_2$

Work Step by Step

We are given: $T(2v_1+3v_2)=v_1+v_2 \\ T(v_1+v_2)=3v_1-v_2$ Thus: $2T(v_1)+3T)v_2)=v_1+v_2\\ T(v_1)+T(v_2)=3v_1-v_2$ Thus: $T(v_1)=8v_1-4v_2\\ T(v_2)=-5v_1+3v_2$

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