Problem 1. Consider C([-π, π]) with the inner-product and S ≤ C([−,π]) be CπT (f\9)= | | f(x)g(x)dx 2πT S = {sin(nx), cos(mx) : m, n > 0}, verify that S is an orthogonal set in C([-π, π]). Some trigonometry identities that might be useful are: sin(A) sin(B) = [cos(A – B) – cos(A + B)] and cos(A) cos(B) = [cos(A - B) + cos(A + B)] _ 2 2 Perform the Gram-Schmidt method on (sin(x), cos(x), x, x²) in the inner product space C([-π,π]) with the inner-product from problem 1.
Problem 1. Consider C([-π, π]) with the inner-product and S ≤ C([−,π]) be CπT (f\9)= | | f(x)g(x)dx 2πT S = {sin(nx), cos(mx) : m, n > 0}, verify that S is an orthogonal set in C([-π, π]). Some trigonometry identities that might be useful are: sin(A) sin(B) = [cos(A – B) – cos(A + B)] and cos(A) cos(B) = [cos(A - B) + cos(A + B)] _ 2 2 Perform the Gram-Schmidt method on (sin(x), cos(x), x, x²) in the inner product space C([-π,π]) with the inner-product from problem 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![Problem 1. Consider C([-π, π]) with the inner-product
and S ≤ C([−,π]) be
CπT
(f\9)= | | f(x)g(x)dx
2πT
S = {sin(nx), cos(mx) : m, n > 0},
verify that S is an orthogonal set in C([-π, π]). Some trigonometry identities that might be
useful are:
sin(A) sin(B)
=
[cos(A – B) – cos(A + B)] and
cos(A) cos(B) = [cos(A - B) + cos(A + B)]
_
2
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4217e83c-b4b2-47da-9d7a-2d6031448fca%2Fb5f08527-d087-403f-a80a-3b905da11352%2Fj2ar2kg_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 1. Consider C([-π, π]) with the inner-product
and S ≤ C([−,π]) be
CπT
(f\9)= | | f(x)g(x)dx
2πT
S = {sin(nx), cos(mx) : m, n > 0},
verify that S is an orthogonal set in C([-π, π]). Some trigonometry identities that might be
useful are:
sin(A) sin(B)
=
[cos(A – B) – cos(A + B)] and
cos(A) cos(B) = [cos(A - B) + cos(A + B)]
_
2
2
![Perform the Gram-Schmidt method on (sin(x), cos(x), x, x²) in the inner product space C([-π,π])
with the inner-product from problem 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4217e83c-b4b2-47da-9d7a-2d6031448fca%2Fb5f08527-d087-403f-a80a-3b905da11352%2F7g9loob_processed.png&w=3840&q=75)
Transcribed Image Text:Perform the Gram-Schmidt method on (sin(x), cos(x), x, x²) in the inner product space C([-π,π])
with the inner-product from problem 1.
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