Answer
$2$
Work Step by Step
According to the Sum of Rank and Nullity Theorem (the sum of the rank and the nullity of $T$ equal the dimension of the domain),
$Rank(T)=dim(P_5)-nullity(T)=(5+1)-4=2$.
Elementary Linear Algebra 7th Edition
by Larson, Ron
Published by
Cengage Learning
ISBN 10:
1-13311-087-8
ISBN 13:
978-1-13311-087-3
Chapter 6 - Linear Transformations - Review Exercises - Page 337: 36
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