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-1², 2+t+t², +8t-3t² Does the set of polynomials span P₂? OA. Yes; since the matrix whose columns are the B-coordinate vectors of each polynomial has a pivot position each row, the set of coordinate vectors spans R². By isomorphism between R² and P2, the set of polynomials spans P₂. OB. 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 matrix whose columns are the B-coordinate vectors of each polynomial has a pivot position each row, the set of coordinate vectors spans R³. By isomorphism between R³ and P2, the set of polynomials spans P₂.

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-1², 2+t+t², +8t-3t² Does the set of polynomials span P₂? OA. Yes; since the matrix whose columns are the B-coordinate vectors of each polynomial has a pivot position each row, the set of coordinate vectors spans R². By isomorphism between R² and P2, the set of polynomials spans P₂. OB. 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 matrix whose columns are the B-coordinate vectors of each polynomial has a pivot position each row, the set of coordinate vectors spans R³. By isomorphism between R³ and P2, the set of polynomials spans P₂.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 46E

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