Let B be the standard basis of the space P, of polynomials.Use coordinate vectors to test whether the following set of polynomials span P,. Justify your conclusion.1-2t + 3, -4+6t – 81, -2+3t - 4?, 2- 3t + 412Does the set of polynomials span P,?O A. 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 R°. By isomorphismbetween R and P, , the set of polynomials does not span P,.O B. 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 P,, the set of polynomials spans P2-O C. 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 isomorphismbetween R2 and P,, the set of polynomials does not span P,.O 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 R2. By isomorphism between R2 and P,the set of polynomials spans P2.

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B be the standard basis of the space P, of polynomials.Use coordinate vectors to test whether the following set of polynomials span P2. Justify your conclusion. 1-2t + 312, -4 + 6t – 81², - 2+3t - 412, 2- 31 + 412 es the set of polynomials span P2? A. 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 R. By isomorphism between R and P, , the set of polynomials does not span P2. B. Yes; since the matrix whose columns are the B-coordinate vectors of each polynomial has , the set of polynomials spans P2. pivot position in each row, the set of coordinate vectors spans R3. By isomorphism between R3 and C. 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 R 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 ,the set of polynomials spans P2. pivot position in each row, the set of coordinate vectors spans R2. By isomorphism between R2 and

B be the standard basis of the space P, of polynomials.Use coordinate vectors to test whether the following set of polynomials span P2. Justify your conclusion. 1-2t + 312, -4 + 6t – 81², - 2+3t - 412, 2- 31 + 412 es the set of polynomials span P2? A. 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 R. By isomorphism between R and P, , the set of polynomials does not span P2. B. Yes; since the matrix whose columns are the B-coordinate vectors of each polynomial has , the set of polynomials spans P2. pivot position in each row, the set of coordinate vectors spans R3. By isomorphism between R3 and C. 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 R 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 ,the set of polynomials spans P2. pivot position in each row, the set of coordinate vectors spans R2. By isomorphism between R2 and

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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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Let B be the standard basis of the space P, of polynomials.Use coordinate vectors to test whether the following set of polynomials span P,. Justify your conclusion.
1-2t + 3, -4+6t – 81, -2+3t - 4?, 2- 3t + 412
Does the set of polynomials span P,?
O A. 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 R°. By isomorphism
between R and P, , the set of polynomials does not span P,.
O B. 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 P,
, the set of polynomials spans P2-
O C. 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 P,, the set of polynomials does not span P,.
O 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 R2. By isomorphism between R2 and P,
the set of polynomials spans P2.

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