2 Consider the set S = {x² + 1, 2x − 2, −x² + x}. The set S spans P2. If t(x) = 5x² + x + 2 € P₂, then t can be written as a linear combination of elements of S. That is, t(x) = Determine a, b, and c a = = a · (x² + 1) + b · (2x − 2) + c · (–x² + x). b = C = Question Help: Video Message instructor Post to forum
2 Consider the set S = {x² + 1, 2x − 2, −x² + x}. The set S spans P2. If t(x) = 5x² + x + 2 € P₂, then t can be written as a linear combination of elements of S. That is, t(x) = Determine a, b, and c a = = a · (x² + 1) + b · (2x − 2) + c · (–x² + x). b = C = Question Help: Video Message instructor Post to forum
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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Question
![2
Consider the set S = {x² + 1, 2x − 2, −x² + x}. The set S spans P2.
If t(x) = 5x² + x + 2 € P₂,
then t can be written as a
linear combination of elements of S.
That is,
t(x) =
Determine a, b, and c
a =
= a ·
(x² + 1) + b · (2x − 2) + c · (–x² + x).
b
=
C =
Question Help: Video Message instructor Post to forum](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65ce4946-20f3-402b-8a73-35e62e74d93e%2Fc6c241f3-b679-4ae7-9061-de1e3377d5c7%2F1pf1r7_processed.png&w=3840&q=75)
Transcribed Image Text:2
Consider the set S = {x² + 1, 2x − 2, −x² + x}. The set S spans P2.
If t(x) = 5x² + x + 2 € P₂,
then t can be written as a
linear combination of elements of S.
That is,
t(x) =
Determine a, b, and c
a =
= a ·
(x² + 1) + b · (2x − 2) + c · (–x² + x).
b
=
C =
Question Help: Video Message instructor Post to forum
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