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) = −p(t) for all t}B. {p(t) | p(2) = 7}c. {p(t) | p′ (7) = p(3)}D. {p(t) | p' (t) is constant}E. {p(t) \ Jốp(t)dt = 0}Ƒ. {p(t) | p' (t) + 6p(t) + 2 = 0}

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Answered: Let P₂ denote the vector space of…

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? p(t) | p(−t) = −p(t) for all t} (t) |p(2) = 7} (t) | p' (7) = p(3)}