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(1) = 3}B. {p(t) | p' (8) = p(7)}c. {p(t) | p(−t) = p(t) for all t}D. {p(t) | p' (t) is constant}Ē. {p(t) | p' (t) + 6p(t)+7=0}OF. {p(t) |p(5)=0}

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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 vector space of polynomials of degree up to 2. Which of the following subsets of P₂ are subspaces of P₂? A. {p(t) |p(1) = 3} B. {p(t) | p' (8) = p(7)} c. {p(t) | p(−t) = p(t) for all t}