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. 1-2t+3², -t+21², -2-1+41², 4-6t+81² C 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 in each row, the set of coordinate vectors spans R³. By isomorphism between R³ 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. 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. OD. 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 R²2 and P₂, the set of polynomials does not span 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. 1-2t+3², -t+21², -2-1+41², 4-6t+81² C 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 in each row, the set of coordinate vectors spans R³. By isomorphism between R³ 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. 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. OD. 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 R²2 and P₂, the set of polynomials does not span P₂.

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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