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}

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) +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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