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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) + 2p(t) + 5 = 0} B. {p(t)| f³ p(t)dt = 0} 3 ○c. {p(t) | p' (t) is constant} D. {p(t) | p(7) = 0} ○Ē. {p(t) | p(−t) = p(t) for all t} ○F. {p(t) | p(5) = 8}

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) + 2p(t) + 5 = 0} B. {p(t)| f³ p(t)dt = 0} 3 ○c. {p(t) | p' (t) is constant} D. {p(t) | p(7) = 0} ○Ē. {p(t) | p(−t) = p(t) for all t} ○F. {p(t) | p(5) = 8}

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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) + 2p(t) + 5 = 0} B. {p(t) | ſ³ p(t)dt = 0} 3 ○c. {p(t) | p' (t) is constant} D. {p(t) | p(7) = 0} E. ○Ē. {p(t) | p(−t) = p(t) for all t} ○F. {p(t) | p(5) = 8}
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) + 2p(t) + 5 = 0} B. {p(t) | ſ³ p(t)dt = 0} 3 ○c. {p(t) | p' (t) is constant} D. {p(t) | p(7) = 0} E. ○Ē. {p(t) | p(−t) = p(t) for all t} ○F. {p(t) | p(5) = 8}
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