Consider the following linear map T: P3 → P3 defined as follows: T(ao + a1x+ azx² + a3x³) = ao + a1(r+ 2) + a2(x+ 2)² + a3(x+ 3)³ = (ao + 2a1 + 4a2 + 8a3) + (a1 + 4a2 + 12a3)x + (a2 + 6a3)x² + a3x³ %3D a) Determine if it is an isomorphism. b) Determine if x + 2x² is in the image of T.
Consider the following linear map T: P3 → P3 defined as follows: T(ao + a1x+ azx² + a3x³) = ao + a1(r+ 2) + a2(x+ 2)² + a3(x+ 3)³ = (ao + 2a1 + 4a2 + 8a3) + (a1 + 4a2 + 12a3)x + (a2 + 6a3)x² + a3x³ %3D a) Determine if it is an isomorphism. b) Determine if x + 2x² is in the image of T.
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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![4.
Consider the following linear map
T: P3 → P3
defined as follows:
T(ao + a1x + a2r² + a3x*) = ao + a1(r+ 2) + a2(x+ 2)² + a3(x+3)*
(ao + 2a1 + 4a2 + 8a3) + (a1 + 4az + 12a3)r + (a2 + 6a3)r² + azr
%3D
a) Determine if it is an isomorphism.
b) Determine if r + 2x? is in the image of T.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14815be2-6dae-4474-bc6b-06046c1707f6%2F34f8dffc-f559-4e28-9475-03324aeada81%2Fbgg6npg_processed.png&w=3840&q=75)
Transcribed Image Text:4.
Consider the following linear map
T: P3 → P3
defined as follows:
T(ao + a1x + a2r² + a3x*) = ao + a1(r+ 2) + a2(x+ 2)² + a3(x+3)*
(ao + 2a1 + 4a2 + 8a3) + (a1 + 4az + 12a3)r + (a2 + 6a3)r² + azr
%3D
a) Determine if it is an isomorphism.
b) Determine if r + 2x? is in the image of T.
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