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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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.
1-2t+3t², -t+21², -2-t+41², 4-6t+8t²
Does the set of polynomials span P₂?
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 R³. By isomorphism between R³
and P2, the set of polynomials spans P2.
. By
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. |
isomorphism between R³ and P2, the set of polynomials does not span P2.
C. 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.
D. 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.
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