Assignmen Let p, 0)=2+f,P2(1)=t-4, P3(1) = 4 +t-21 Complete parts and (b) below. a. Use coordinate vectors to show that these polynomials form a basis for P. What are the coordinate vectors corresponding to p,, P2, and p3? 2 P = P2 = Pa = - 2 Place these coordinate vectors into the columns of a matrix A. What can be said about the matrix A? OA The matrix A is invertible because it is row equivalent to la and therefore the row reduced columns of A form a basis for R3 by the Invertible Matrix Theorem. OB. The matrix A is invertible because it is row equivalent tol, and therefore the null space of A, denoted Nul A, forms a basis for R3 by the Invertible Matrix Theorem. OC The matrix A forms a basis for R3 by the Invertible Matriix Theorem because all square matrices are row equivalent to . 0. The matrbx A is invertible because it is row equivalent to l, and therefore the original columns of A form a basis for R3 by the Invertible Matrix Theorem. How does this show that the polynomials form a basis for P2? OA The polynomials form a basis for P, because any basis in Rn is also a basis in P, DB The polynomials form a basis for P, because the columns of A are linearly independent OC The polynomials form a basis for P, because the matrix A is invertible D. The polynomials form a basis for P, because of the isomorphism between R and P. b Consider the basis B= (p,. P2 P3) for P2 Find q in Pa given that [q]e = q)= ( t-C
Assignmen Let p, 0)=2+f,P2(1)=t-4, P3(1) = 4 +t-21 Complete parts and (b) below. a. Use coordinate vectors to show that these polynomials form a basis for P. What are the coordinate vectors corresponding to p,, P2, and p3? 2 P = P2 = Pa = - 2 Place these coordinate vectors into the columns of a matrix A. What can be said about the matrix A? OA The matrix A is invertible because it is row equivalent to la and therefore the row reduced columns of A form a basis for R3 by the Invertible Matrix Theorem. OB. The matrix A is invertible because it is row equivalent tol, and therefore the null space of A, denoted Nul A, forms a basis for R3 by the Invertible Matrix Theorem. OC The matrix A forms a basis for R3 by the Invertible Matriix Theorem because all square matrices are row equivalent to . 0. The matrbx A is invertible because it is row equivalent to l, and therefore the original columns of A form a basis for R3 by the Invertible Matrix Theorem. How does this show that the polynomials form a basis for P2? OA The polynomials form a basis for P, because any basis in Rn is also a basis in P, DB The polynomials form a basis for P, because the columns of A are linearly independent OC The polynomials form a basis for P, because the matrix A is invertible D. The polynomials form a basis for P, because of the isomorphism between R and P. b Consider the basis B= (p,. P2 P3) for P2 Find q in Pa given that [q]e = q)= ( t-C
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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Help needed on the last part b only thanks in advance
![Assignmen
Let p, (1)=2+f, P2(1)=t- 4t², P3(1) = 4 +t- 21². Complete parts (a) and (b) below.
a. Use coordinate vectors to show that these polynomials form a basis for P.
What are the coordinate vectors corresponding to p, , p2, and p3?
4.
P =
P2 =
.P3 =
Place these coordinate vectors into the columns of a matrix A. What can be said about the matrix A?
OA The matrix A is invertible because it is row equivalent to la and therefore the row reduced columns of A form a basis for R³ by the Invertible Matrix Theorem.
O B. The matrix A is invertible because it is row equivalent to |, and therefore the null space of A, denoted Nul A, forms a basis for R3 by the Invertible Matrix Theorem.
OC. The matrix A forms a basis for R3 by the Invertible Matrix Theorem because all square matrices are row equivalent to l,
0. The matrix A is invertible because it is row equivalent to l, and therefore the original columns of A form a basis for R³ by the Invertible Matrix Theorem.
How does this show that the polynomials form a basis for P,?
OA. The polynomials form a basis for P, because any basis in Rr is also a basis in P.
OB The polynomials form a basis for P, because the columns of A are linearly independent.
OC The polynomials form a basis for P, because the matrix A is invertible.
The polynomials form a basis for P, because of the isomorphism between R3 and P.
b. Consider the basis B= (p,. P2. Pa) for P, Find q in P given that [q]e =|
qt) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91ebeefb-4552-4ee2-a18c-1232c59f100f%2F9a510ac8-0549-457c-bdaf-c67990622cfc%2F14lc86_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Assignmen
Let p, (1)=2+f, P2(1)=t- 4t², P3(1) = 4 +t- 21². Complete parts (a) and (b) below.
a. Use coordinate vectors to show that these polynomials form a basis for P.
What are the coordinate vectors corresponding to p, , p2, and p3?
4.
P =
P2 =
.P3 =
Place these coordinate vectors into the columns of a matrix A. What can be said about the matrix A?
OA The matrix A is invertible because it is row equivalent to la and therefore the row reduced columns of A form a basis for R³ by the Invertible Matrix Theorem.
O B. The matrix A is invertible because it is row equivalent to |, and therefore the null space of A, denoted Nul A, forms a basis for R3 by the Invertible Matrix Theorem.
OC. The matrix A forms a basis for R3 by the Invertible Matrix Theorem because all square matrices are row equivalent to l,
0. The matrix A is invertible because it is row equivalent to l, and therefore the original columns of A form a basis for R³ by the Invertible Matrix Theorem.
How does this show that the polynomials form a basis for P,?
OA. The polynomials form a basis for P, because any basis in Rr is also a basis in P.
OB The polynomials form a basis for P, because the columns of A are linearly independent.
OC The polynomials form a basis for P, because the matrix A is invertible.
The polynomials form a basis for P, because of the isomorphism between R3 and P.
b. Consider the basis B= (p,. P2. Pa) for P, Find q in P given that [q]e =|
qt) =
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