Let P2 denote the vector space of polynomials of degree up to 2. Which of the following subsets of P2 are subspaces of P2? A. {p(t) | p′(t)+9p(t)+2=0} B. {p(t) | p(7)=3} C. {p(t) | p(−t)=−p(t) for all t} D. {p(t) | p′(5)=p(0)} E. {p(t) | ∫30p(t)dt=0} F. {p(t) | p(6)=0}
Let P2 denote the vector space of polynomials of degree up to 2. Which of the following subsets of P2 are subspaces of P2? A. {p(t) | p′(t)+9p(t)+2=0} B. {p(t) | p(7)=3} C. {p(t) | p(−t)=−p(t) for all t} D. {p(t) | p′(5)=p(0)} E. {p(t) | ∫30p(t)dt=0} F. {p(t) | p(6)=0}
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.3: Subspaces Of Vector Spaces
Problem 45E: Consider the vector spaces P0,P1,P2,...,Pn where Pk is the set of all polynomials of degree less...
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Let P2 denote the
A. {p(t) | p′(t)+9p(t)+2=0}
B. {p(t) | p(7)=3}
C. {p(t) | p(−t)=−p(t) for all t}
D. {p(t) | p′(5)=p(0)}
E. {p(t) | ∫30p(t)dt=0}
F. {p(t) | p(6)=0}
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