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.
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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Transcribed Image Text: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 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.
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