(d) sin(x) and cos²(x) in C([-T, π]) with the inner-product from (c). (e) (1,2,3) and (−1, 1, 1) in R³ with the inner-product (y) below. = Ay where A is as (f) (1,2,3) and (1, 1, −2) in R³ with the the inner-product (˜|y) = x³ Aỹ where A is as below. 6 1 0 A = 16 0 0 08/3 For each of the following pairs of vectors, find the inner-product in the specified inner-product space and determine if they are orthogonal. (a) (1,2,3) and (−1, 1, 1)† in R³ with the usual dot-product · y=xТỹ. (b) (1,2,3) and (1,1, −2) in R³ with the usual dot-product. (c) sin(x) and cos(x) in the C([-π, π]) with the inner-product (f|g) 1 CπT = f(x)g(x)dx. 2πT -π •
(d) sin(x) and cos²(x) in C([-T, π]) with the inner-product from (c). (e) (1,2,3) and (−1, 1, 1) in R³ with the inner-product (y) below. = Ay where A is as (f) (1,2,3) and (1, 1, −2) in R³ with the the inner-product (˜|y) = x³ Aỹ where A is as below. 6 1 0 A = 16 0 0 08/3 For each of the following pairs of vectors, find the inner-product in the specified inner-product space and determine if they are orthogonal. (a) (1,2,3) and (−1, 1, 1)† in R³ with the usual dot-product · y=xТỹ. (b) (1,2,3) and (1,1, −2) in R³ with the usual dot-product. (c) sin(x) and cos(x) in the C([-π, π]) with the inner-product (f|g) 1 CπT = f(x)g(x)dx. 2πT -π •
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please help with parts d,e,f with solution and steps!
![(d) sin(x) and cos²(x) in C([-T, π]) with the inner-product from (c).
(e) (1,2,3) and (−1, 1, 1) in R³ with the inner-product (y)
below.
=
Ay where A is as
(f) (1,2,3) and (1, 1, −2) in R³ with the the inner-product (˜|y) = x³ Aỹ where A is as
below.
6 1 0
A = 16 0
0 08/3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F781395ef-5933-4a4d-9640-3099b49e30d5%2Fbb87209a-7a20-4f9e-8f7f-bf1303fd5d0f%2F2jl3een_processed.png&w=3840&q=75)
Transcribed Image Text:(d) sin(x) and cos²(x) in C([-T, π]) with the inner-product from (c).
(e) (1,2,3) and (−1, 1, 1) in R³ with the inner-product (y)
below.
=
Ay where A is as
(f) (1,2,3) and (1, 1, −2) in R³ with the the inner-product (˜|y) = x³ Aỹ where A is as
below.
6 1 0
A = 16 0
0 08/3
![For each of the following pairs of vectors, find the inner-product in the specified inner-product
space and determine if they are orthogonal.
(a) (1,2,3) and (−1, 1, 1)† in R³ with the usual dot-product · y=xТỹ.
(b) (1,2,3) and (1,1, −2) in R³ with the usual dot-product.
(c) sin(x) and cos(x) in the C([-π, π]) with the inner-product
(f|g)
1
CπT
=
f(x)g(x)dx.
2πT
-π
•](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F781395ef-5933-4a4d-9640-3099b49e30d5%2Fbb87209a-7a20-4f9e-8f7f-bf1303fd5d0f%2Fw4woorj_processed.png&w=3840&q=75)
Transcribed Image Text:For each of the following pairs of vectors, find the inner-product in the specified inner-product
space and determine if they are orthogonal.
(a) (1,2,3) and (−1, 1, 1)† in R³ with the usual dot-product · y=xТỹ.
(b) (1,2,3) and (1,1, −2) in R³ with the usual dot-product.
(c) sin(x) and cos(x) in the C([-π, π]) with the inner-product
(f|g)
1
CπT
=
f(x)g(x)dx.
2πT
-π
•
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