Differential Equations and Linear Algebra (4th Edition)

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: 31

Answer

$bx^2+x(3a+c)+(2a-b+c)$

Work Step by Step

We are given: $T(1)=x+1 \\ T(x)=x^2-1\\ T(x^2)=3x+2$ We obtain: $$T(ax^2+bx+c)=T(ax^2)+T(bx)+T(c)\\ =aT(x^2)+bT(x)+cT(1)\\ =a(3x+2)+b(x^2-1)+c(x+1)\\ =3ax+2a+bx^2-b+cx+c\\ =bx^2+x(3a+c)+(2a-b+c)$$
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