Let P₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 14x² − 17x + 10, 17x – 19x² – 11 and9x² - 10x + 6.a. The dimension of the subspace H isb. Is {14x² - 17x + 10, 17x - 19x² – 11,9x² – 10x +6} a basis for P₂? choosec. 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

Answered: Image /qna-images/answer/cdd82842-a0d5-4572-9bea-d0bd4a2eb070.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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Using linear algebra, show that G={p1(x)=1−x+x^2, p2(x)=x, p3(x)=x+x^2} is a basis of P2, the vector space of polynomials of degree at most two with real coefficients.
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Let B be the standard basis of the space P₂ of polynomials. Use coordinate vectors to test whether the following set of polynomials span P2. Justify your conclusion. - 5t+t², 1+5t-t²2, 2+t+t², +8t-3t² G Does the set of polynomials span P₂? O A. Yes; since the matrix whose columns are the B-coordinate vectors of each polynomial has a pivot position in each row, the set of coordinate vectors spans R². By isomorphism between R² and P2, the set of polynomials spans P2. O B. No; since the matrix whose columns are the B-coordinate vectors of each polynomial does not have a pivot position in each row, the set of coordinate vectors does not span R³. By isomorphism between R³ and P2, the set of polynomials does not span P2. OC. No; since the matrix whose columns are the B-coordinate vectors of each polynomial does not have a pivot position in each row, the set of coordinate vectors does not span R². By isomorphism between R² and P2, the set of polynomials does not span P2. ⒸD. Yes; since the…
Let P₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 2x27x-4,- (2x + 1) and 2x² + x. a. The dimension of the subspace H is b. Is {2x27x-4,- (2x + 1), 2x² + x} a basis for P₂ ✓ choose basis for P_2 not a basis for P_2 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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