A condition on the coefficients of a polynomial aº + a₁x+ a²x² + a²×³ is given. Determine whether or not the set of all such polynomials satisfying this condition is a3subspace of the space P of all polynomials.ao + a₁ + a₂ + a3 = 0Choose the correct answer below.A. The set is not a subspace of P. The set contains the zero polynomial, and the set is closed under multiplication by scalars, but the set is not closed underaddition.B. The set is not a subspace of P. The set does not contain the zero polynomial.C. The set is a subspace of P. The set contains the zero polynomial, the set is closed under addition of scalars, and the set is closed under multiplication by scalars.D. The set is not a subspace of P. The set contains the zero polynomial, and the set is closed under addition, but the set is not closed under multiplication byscalars.E. The set is a subspace of P. The set contains the zero polynomial, and the set is closed under the formation of linear combinations of its elements.

Solution:- The correct option (B) The set is not a subspace of P . the set does not contain the zero…

Answered: A condition on the coefficients of a…

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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4.
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Let P₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 1 - 4x², 11- (6x² +7x) and x=x²-1. a. The dimension of the subspace His b. Is {1 - 4x², 11- (6x² +7x),x-x² - 1} a basis for P₂? choose c. A basis for the subspace H is { (where you can enter xx in place of x²) Be sure you can explain and justify your answer. }. Enter a polynomial or a comma separated list of polynomials
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Which of the following is a subspace of the vector space P2 of all polynomials of degree at most 2? Select one or more: O a. The set of all polynomials of degree at most 1 O b. {ao +a1r + a2x2 E P2 : ao = 4} Oc. {ao +a1r + a2x E P2: a1 + a2 = 3} %3D d. {1+x+ x}

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