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 - 6.6 Chapter Review - Additional Problems - Page 430: 16

Answer

$dim[Ker(T)]=2$

Work Step by Step

Since $T:P_5(R) \rightarrow M_2(R)$, we can obtain: $Rng(T)=M_2(R)\\ \rightarrow dim[Rng(T)]=dim[M_2(R)]=4$ According to Rank-Nullity Theorem: $dim[Ker(T)]+dim[Rng(T)]=dim[P_5(R)] \\ dim[Ker(T)]+4=6\\ dim[Ker(T)]=2$
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