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)}
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)}
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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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) = −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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