Find the Fourier coefficient c and the projection cw of v along w for each of the following. (а) v — (1,3, 1, 2) and w = (1, –2, 7,4) in R4. (b) v = : t² and w =t+ 3 in P(t), with inner product (f(t), g(t)) = So f(t)g(t) dt. 1 (c) v = 2 and w = 1 in M2,2 (R), inner product defined by (A, B) = tr(B" A). 3 4 5 5
Find the Fourier coefficient c and the projection cw of v along w for each of the following. (а) v — (1,3, 1, 2) and w = (1, –2, 7,4) in R4. (b) v = : t² and w =t+ 3 in P(t), with inner product (f(t), g(t)) = So f(t)g(t) dt. 1 (c) v = 2 and w = 1 in M2,2 (R), inner product defined by (A, B) = tr(B" A). 3 4 5 5
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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![Find the Fourier coefficient c and the projection cw of v along w for each of the following.
(1,3, 1, 2) and w
(1, –2, 7,4) in R4.
(а) у —
(b) v =
t² and w =t+3 in P(t), with inner product (f(t), g(t)) = So f(t)g(t) dt.
1
(c) v =
[:]
2
and w =
1
1
in M2,2 (R), inner product defined by (A, B) = tr(B" A).
3 4
5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6214fda8-f992-4e88-b320-5195339361f5%2Fa6703074-578b-401e-8944-66c5124d2247%2F8d69wy_processed.png&w=3840&q=75)
Transcribed Image Text:Find the Fourier coefficient c and the projection cw of v along w for each of the following.
(1,3, 1, 2) and w
(1, –2, 7,4) in R4.
(а) у —
(b) v =
t² and w =t+3 in P(t), with inner product (f(t), g(t)) = So f(t)g(t) dt.
1
(c) v =
[:]
2
and w =
1
1
in M2,2 (R), inner product defined by (A, B) = tr(B" A).
3 4
5
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