Let P₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spannedby 9x² - 12x – 11, 3 — (x² + x) and 4x² – 5x – 5.a. The dimension of the subspace Hisb. Is {9x² - 12x - 11,3 — (x² + x), 4x² - 5x -5} a basis for P₂? choosesure you can explain and justify your answer.c. A basis for the subspace H is {polynomial or a comma separated list of polynomials.Enter aBe

Answered: Image /qna-images/answer/8d82ce7f-329f-49d2-ace4-4d1bcef3c66f.jpg

Answered: Let P₂ be the vector space of all…

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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Consider the basis B= {1, x+x?, 2x²-1} for the vector space P2. The coordinate vector of the polynomial p(x) = 7 + 5x + 4x2 relative to B is B
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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 - 3x + 2, 12x – 7x2 – 2 and 3x2 – 3x + 1. 5x2 a. The dimension of the subspace H is b. Is {5æ? . - 3x + 2, 12x – 7x? – 2, 3x? – 3x + 1} a basis for P2? c. A basis for the subspace H is {
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