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 C {1, x, x², x³}, {-2+x+x²,2- 2x - x², 1+x}, 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] = 0000 0000 0000
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 C {1, x, x², x³}, {-2+x+x²,2- 2x - x², 1+x}, 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] = 0000 0000 0000
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Ll.118.
![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
C
{1, x, x², x³},
-
{−2+x+x²,2 − 2x − x², 1+x},
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] =
0000
0000
0000](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3320653f-3c42-4576-805c-19d46b0a4388%2F15c90268-8996-4ce0-8c29-8c7947396b46%2F6gojii_processed.jpeg&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
C
{1, x, x², x³},
-
{−2+x+x²,2 − 2x − x², 1+x},
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] =
0000
0000
0000
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