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Let P₂ denote the vector space of polynomials of degree up to 2. Which of the following absets of P₂ are subspaces of P2? A. {p(t) | p' (t) + 8p(t) + 4 = 0} B. {p(t) | p(4) = 0} c. {p(t)| Sop(t)dt = 0} D. {p(t) | p (8) = P(2)} E. {p(t) |p(-t) = p(t) for all t} OF. {p(t) |p(0) = 7}

Let P₂ denote the vector space of polynomials of degree up to 2. Which of the following absets of P₂ are subspaces of P2? A. {p(t) | p' (t) + 8p(t) + 4 = 0} B. {p(t) | p(4) = 0} c. {p(t)| Sop(t)dt = 0} D. {p(t) | p (8) = P(2)} E. {p(t) |p(-t) = p(t) for all t} OF. {p(t) |p(0) = 7}

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? A. {p(t) | p' (t) +8p(t) + 4 = 0} B. {p(t) | p(4) = 0} Oc. {p(t) p(t)dt = 0} D. {p(t) | p' (8) = p(2)} OE. {p(t) |p(-t) = p(t) for all t} OF. {p(t)|p(0) = 7}
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? A. {p(t) | p' (t) +8p(t) + 4 = 0} B. {p(t) | p(4) = 0} Oc. {p(t) p(t)dt = 0} D. {p(t) | p' (8) = p(2)} OE. {p(t) |p(-t) = p(t) for all t} OF. {p(t)|p(0) = 7}
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