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}
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?
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ff93d80-f747-4f15-803d-56788ff3d116%2Fb7529081-60d0-440e-b57e-384cf8f421c6%2F3mjuzq8_processed.png&w=3840&q=75)
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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