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}

Answered: Let P₂ denote the vector space of…

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' (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}