Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 1 - Linear Equations in Linear Algebra - 1.8 Exercises - Page 70: 24

Answer

$T(x) = c_1T(v_1)+...+c_pT(v_p) = c10+...+c_p0 = 0$

Work Step by Step

Given any x in $R^n$, there are constants $c_1,...,c_p$ such that $x= c_1v_1+ ... c_pV_p$ because $v_1,...,v_p$ span $R_n$. Thus, using property(5) of a linear transformation.
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