5. Consider the space P2 (the space of polynomials of degree at most 2) and define the inner product 1 (p, q) = = (p(0)q(0) + p(1)q(1) + p(2)q(2)).
5. Consider the space P2 (the space of polynomials of degree at most 2) and define the inner product 1 (p, q) = = (p(0)q(0) + p(1)q(1) + p(2)q(2)).
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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(a) Show that the standard basis {1, x, x^2} is not orthogonal with respect to this inner product.
(b) (15) Use the standard basis {1, x, x^2} to find an orthonormal basis for this inner product space.
!["5. Consider the space \( P_2 \) (the space of polynomials of degree at most 2) and define the inner product
\[
\langle p, q \rangle = \frac{1}{3} \left( p(0)q(0) + p(1)q(1) + p(2)q(2) \right).
\]"](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f84e8f7-b971-450c-a485-c719bf1153d8%2F5f90e555-e559-43f6-8555-c3c3b645a428%2Fqlac89l_processed.png&w=3840&q=75)
Transcribed Image Text:"5. Consider the space \( P_2 \) (the space of polynomials of degree at most 2) and define the inner product
\[
\langle p, q \rangle = \frac{1}{3} \left( p(0)q(0) + p(1)q(1) + p(2)q(2) \right).
\]"
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