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' (6) = p(1)} | B. {p(t) | p(8) = 9} c. {p(t) | p' (t) is constant} D. {p(t) | Sp(t)dt = 0} E. {p(t) | p' (t) + 3p(t) + 2 = 0} OF. {p(t) | p(7) = 0}

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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' (6) = p(1)}
| B. {p(t) | p(8) = 9}
C. {p(t) | p' (t) is constant }
2
| D. {p(t) | √² p(t)dt = 0}
E. {p(t) | p' (t) + 3p(t) + 2 = 0}
| F. {p(t) | p(7) = 0}
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' (6) = p(1)} | B. {p(t) | p(8) = 9} C. {p(t) | p' (t) is constant } 2 | D. {p(t) | √² p(t)dt = 0} E. {p(t) | p' (t) + 3p(t) + 2 = 0} | F. {p(t) | p(7) = 0}
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