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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′ (7) = p(3)} |B. {p(t) | ſ p(t)dt = 0} □C. {p(t) | p' (t) + 6p(t) + 9 = 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′ (7) = p(3)} |B. {p(t) | ſ p(t)dt = 0} □C. {p(t) | p' (t) + 6p(t) + 9 = 0}

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 28E
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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? JA. {p(t) \ p′ (7) = p(3)} JB. {p(t) \ fo° p(t)dt = 0} C. {p(t) | p′ (t) + 6p(t) + 9 = 0} □D. {p(t) | p(−t) = p(t) for all t} | E. {p(t) | p(5) = 0} ]F. {p(t) | p(0) = 4} 00 UUUL
Transcribed Image Text:Let P₂ denote the vector space of polynomials of degree up to 2. Which of the following subsets of P2 are subspaces of P₂? JA. {p(t) \ p′ (7) = p(3)} JB. {p(t) \ fo° p(t)dt = 0} C. {p(t) | p′ (t) + 6p(t) + 9 = 0} □D. {p(t) | p(−t) = p(t) for all t} | E. {p(t) | p(5) = 0} ]F. {p(t) | p(0) = 4} 00 UUUL
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