Let Pn be the vector space of all polynomials of degree n or less in the variable x. Let D : P3 → P₂ be the linear transformation defined D(p(x)) = p' (x). That is, D is the derivative operator. Let { 1, x, x², x³ }, {1, x, x²}, be ordered bases for P3 and P2, respectively. Find the matrix [D] for D relative to the basis B in the domain and C in the codomain. [D] = B C = =
Let Pn be the vector space of all polynomials of degree n or less in the variable x. Let D : P3 → P₂ be the linear transformation defined D(p(x)) = p' (x). That is, D is the derivative operator. Let { 1, x, x², x³ }, {1, x, x²}, be ordered bases for P3 and P2, respectively. Find the matrix [D] for D relative to the basis B in the domain and C in the codomain. [D] = B C = =
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 11CM
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Question
![Let Pn be the vector space of all polynomials of degree n or less in the variable x. Let D : P3 → P₂ be the linear transformation defined by
D(p(x)) = p′ (x). That is, D is the derivative operator. Let
B
{ 1, x, x², x³ },
{1, x, x²},
C
be ordered bases for P3 and P2, respectively. Find the matrix [D] for D relative to the basis B in the domain and C in the codomain.
[D] =
=
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d084809-1178-4503-9f07-a3e1167e0479%2F9423cd4a-b45c-43ff-b0d1-caff7a1b0464%2Fm55gwm_processed.png&w=3840&q=75)
Transcribed Image Text:Let Pn be the vector space of all polynomials of degree n or less in the variable x. Let D : P3 → P₂ be the linear transformation defined by
D(p(x)) = p′ (x). That is, D is the derivative operator. Let
B
{ 1, x, x², x³ },
{1, x, x²},
C
be ordered bases for P3 and P2, respectively. Find the matrix [D] for D relative to the basis B in the domain and C in the codomain.
[D] =
=
=
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