Which of the following subsets of the vector space P2 of polynomials of degree up to two are subspaces? A. {p(t) | p′(5) = p(3)} B. {p(t) | p′(t) + 7p(t) + 6 = 0} C. {p(t) | p′(t) is constant } D. {p(t) | p(0) = 1} E. {p(t) | p(−t) = p(t) for all t} F. {p(t) | p(1) = 0}

Which of the following subsets of the vector space P2 of polynomials of degree up to two are subspaces? A. {p(t) | p′(5) = p(3)} B. {p(t) | p′(t) + 7p(t) + 6 = 0} C. {p(t) | p′(t) is constant } D. {p(t) | p(0) = 1} E. {p(t) | p(−t) = p(t) for all t} F. {p(t) | p(1) = 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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Question

Which of the following subsets of the vector space P₂ of polynomials of degree up to two are subspaces?

A. {p(t) | p′(5) = p(3)}

B. {p(t) | p′(t) + 7p(t) + 6 = 0}

C. {p(t) | p′(t) is constant }

D. {p(t) | p(0) = 1}

E. {p(t) | p(−t) = p(t) for all t}

F. {p(t) | p(1) = 0}

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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