Let V be the vector space of functions spanned by B = {b₁ = 6 sin x + 7 cos x, b₂ = 5 sin x + 3 cos x} where x C = {c₁ = sin x, C₂ = cos x} where x of coordinates matrix P C-B P = C-B Ex: 8 [f(x)]c = Ex: 8 nn 2 The coordinates of a function f(a) relative to the basis Bare [ƒ(*)] = [₁] coordinates of f(x) relative to C and find f(x). f(x) = Ex: 8 nn ,n € Z is also a basis for V. Find the change 2 sin x + ,ne Z COS X Find the
Let V be the vector space of functions spanned by B = {b₁ = 6 sin x + 7 cos x, b₂ = 5 sin x + 3 cos x} where x C = {c₁ = sin x, C₂ = cos x} where x of coordinates matrix P C-B P = C-B Ex: 8 [f(x)]c = Ex: 8 nn 2 The coordinates of a function f(a) relative to the basis Bare [ƒ(*)] = [₁] coordinates of f(x) relative to C and find f(x). f(x) = Ex: 8 nn ,n € Z is also a basis for V. Find the change 2 sin x + ,ne Z 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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Question
![Let V be the vector space of functions spanned by
NLT
B = {b₁ = 6 sin x + 7 cos x, b₂ = 5 sin x + 3 cos x} where x
z z a f
2
C={c₁= sinx, C₂ = cos x} where x A
, ne Z is also a basis for V. Find the change
2
of coordinates matrix P
C-B
P
C+B
Ex: 8
The coordinates of a function f(x) relative to the basis B are [f(x)]B
coordinates of f(x) relative to C and find f(x).
f(x) = Ex: 8
Ex: 8
[f(x)]c
[ƒ(2²)le = []
sin a t
in E Z
4
[3]
0
COST
Find the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97fa71a9-ddb9-496b-9b0a-bf970e388fad%2F7d0c0bcb-f249-40d4-b7b5-67f887a44172%2Fcsdb96_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let V be the vector space of functions spanned by
NLT
B = {b₁ = 6 sin x + 7 cos x, b₂ = 5 sin x + 3 cos x} where x
z z a f
2
C={c₁= sinx, C₂ = cos x} where x A
, ne Z is also a basis for V. Find the change
2
of coordinates matrix P
C-B
P
C+B
Ex: 8
The coordinates of a function f(x) relative to the basis B are [f(x)]B
coordinates of f(x) relative to C and find f(x).
f(x) = Ex: 8
Ex: 8
[f(x)]c
[ƒ(2²)le = []
sin a t
in E Z
4
[3]
0
COST
Find the
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