Let V be the vector space of functions spanned by Nπ B = {b₁ = 5 sin x + 7 cos x, b₂ = 3 sin x + 9 cos x} where x # C = {c₁= sinx, C₂ of coordinates matrix P C+B P = C+B Ex: 6 nn 2,NEZ cos x} where x # 2n € Z is also a basis for V. Find the change -, The coordinates of a function f(x) relative to the basis B3 are [f(x)]B coordinates of f(x) relative to C and find f(x). f(x) = Ex: 6 [f(x)]c = = Ex: 6 sin x + = [3] COS X Find the
Let V be the vector space of functions spanned by Nπ B = {b₁ = 5 sin x + 7 cos x, b₂ = 3 sin x + 9 cos x} where x # C = {c₁= sinx, C₂ of coordinates matrix P C+B P = C+B Ex: 6 nn 2,NEZ cos x} where x # 2n € Z is also a basis for V. Find the change -, The coordinates of a function f(x) relative to the basis B3 are [f(x)]B coordinates of f(x) relative to C and find f(x). f(x) = Ex: 6 [f(x)]c = = Ex: 6 sin x + = [3] COS X Find the
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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![Let V be the vector space of functions spanned by
B = {b₁ = 5 sin x + 7 cos x, b₂ = 3 sin x + 9 cos x} where x
C = {c₁ = sinx, C₂ = cos x} where x =
of coordinates matrix P.
C+B
P =
C+B
Ex: 6
[f(x)] c
The coordinates of a function f(x) relative to the basis B3 are [f(x)] B
=
coordinates of f(x) relative to C and find f(x).
f(x) = Ex: 6
=
Ex: 6
Nπ
2
nn
,n € Z is also a basis for V. Find the change
2
sin x +
,ne Z.
2
[3]
4
COS X
Find the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F974a6490-992c-41a2-b80f-51ad98fb1a32%2F3fbf54fd-d062-4975-a6bd-07a022c04588%2F3marewe_processed.png&w=3840&q=75)
Transcribed Image Text:Let V be the vector space of functions spanned by
B = {b₁ = 5 sin x + 7 cos x, b₂ = 3 sin x + 9 cos x} where x
C = {c₁ = sinx, C₂ = cos x} where x =
of coordinates matrix P.
C+B
P =
C+B
Ex: 6
[f(x)] c
The coordinates of a function f(x) relative to the basis B3 are [f(x)] B
=
coordinates of f(x) relative to C and find f(x).
f(x) = Ex: 6
=
Ex: 6
Nπ
2
nn
,n € Z is also a basis for V. Find the change
2
sin x +
,ne Z.
2
[3]
4
COS X
Find the
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