12. 13. 14. 15. 16. 17. 19. 21. 22. 23. 24. 25. 27. 28. (-1, 4), (1, 3), (3, 0) (-4, 2), (-3, 1), (-2, -1), (-1, -2), (0, -4) (-3,-5), (-2, -3), (-1,-4), (0, -1), (1, -2) (1, 1), (2, 1), (3, 2), (4,2) (-1, 4), (0, 2), (1, 1), (2, 1) In Exercises 17-26, apply the Gram-Schmidt process to the given vectors. (1, 1), (1, 2) 140 18. (2, 0, 2, 1), (1, 0, -2, -2), (2, 1, 1, -1) (1, 1, 1, 1), (1, 2, 1, 0), (1, 3, 0, 0) In Exercises 23 and 24, use f. g = 20. = [₁₁ f(x) n = 1, 2, .... f₁(x) = 1, f₂(x) = x, f3(x) = x² 8₁(x) = 1 x, g₂(x) = 1 + x, g3(x) = 1 + x + x² = In Exercises 27 and 28, use f g (1, 1, 0, 0), (0, 1, 1, 0), (1, 0, 1, 1) f(x)g (x) dx. In Exercises 25 and 26, use A B = a₁₁b₁₁+ a₁2b₁2 + a21b₂1 + a22b₂2. . COCI CIEJ 26. (2π 10 f(x)g (x) dx and let f(x) = sin(nx), Show that fn fm = 0 if n #m. (HINT Use the identity sin u sin v = [cos(u-v) cos(u + v)].) Compute f and produce an infinite collection of orthonormal "vectors."
12. 13. 14. 15. 16. 17. 19. 21. 22. 23. 24. 25. 27. 28. (-1, 4), (1, 3), (3, 0) (-4, 2), (-3, 1), (-2, -1), (-1, -2), (0, -4) (-3,-5), (-2, -3), (-1,-4), (0, -1), (1, -2) (1, 1), (2, 1), (3, 2), (4,2) (-1, 4), (0, 2), (1, 1), (2, 1) In Exercises 17-26, apply the Gram-Schmidt process to the given vectors. (1, 1), (1, 2) 140 18. (2, 0, 2, 1), (1, 0, -2, -2), (2, 1, 1, -1) (1, 1, 1, 1), (1, 2, 1, 0), (1, 3, 0, 0) In Exercises 23 and 24, use f. g = 20. = [₁₁ f(x) n = 1, 2, .... f₁(x) = 1, f₂(x) = x, f3(x) = x² 8₁(x) = 1 x, g₂(x) = 1 + x, g3(x) = 1 + x + x² = In Exercises 27 and 28, use f g (1, 1, 0, 0), (0, 1, 1, 0), (1, 0, 1, 1) f(x)g (x) dx. In Exercises 25 and 26, use A B = a₁₁b₁₁+ a₁2b₁2 + a21b₂1 + a22b₂2. . COCI CIEJ 26. (2π 10 f(x)g (x) dx and let f(x) = sin(nx), Show that fn fm = 0 if n #m. (HINT Use the identity sin u sin v = [cos(u-v) cos(u + v)].) Compute f and produce an infinite collection of orthonormal "vectors."
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
Number 25:
![12.
13.
14.
15.
16.
17. (1, 1), (1, 2)
19.
21.
23.
24.
25.
(-1, 4), (1, 3), (3, 0)
(-4, 2), (-3, 1), (-2, -1), (-1, -2), (0, -4)
(-3,-5), (-2, -3), (-1,-4), (0, -1), (1, -2)
(1, 1), (2, 1), (3, 2), (4, 2)
(-1,4), (0, 2), (1, 1), (2, 1)
In Exercises 17-26, apply the Gram-Schmidt process to the given vectors.
18
27.
800
(2, 0, 2, −1), (1, 0, −2, −2), (2, 1, 1, − 1)
(1, 1, 1, 1), (1, 2, 1, 0), (1, 3, 0, 0)
In Exercises 23 and 24, use f. g
18.
-2
[10] [oo]
n = 1, 2,
20. (1, 1, 0, 0), (0, 1, 1, 0), (1, 0, 1, 1)
= $₁,50
f₁(x) = 1, f₂(x) = x, f3(x) = x²
g₁(x) = 1 - x, g₂(x) = 1 + x, g3(x) = 1 + x + x²
In Exercises 27 and 28, use f. g
In Exercises 25 and 26, use A B = a₁₁b₁₁ + a₁2b₁2 + a21b₂1 + a2222-
●
11
636363
f(x)g (x) dx.
26.
(2π
Lo
f(x)g (x) dx and let f(x) = sin(nx),
Show that fn fm = 0 if n‡m. (HINT Use the identity sin u sin v =
[cos(u - v) - cos(u + v)].)
28. Compute ||f|| and produce an infinite collection of orthonormal "vectors."](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92dd192b-2b85-4e23-91c3-a8e23aec13bb%2F3cb51594-548d-4bff-81b4-082eb045af2c%2Fk87zxtw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:12.
13.
14.
15.
16.
17. (1, 1), (1, 2)
19.
21.
23.
24.
25.
(-1, 4), (1, 3), (3, 0)
(-4, 2), (-3, 1), (-2, -1), (-1, -2), (0, -4)
(-3,-5), (-2, -3), (-1,-4), (0, -1), (1, -2)
(1, 1), (2, 1), (3, 2), (4, 2)
(-1,4), (0, 2), (1, 1), (2, 1)
In Exercises 17-26, apply the Gram-Schmidt process to the given vectors.
18
27.
800
(2, 0, 2, −1), (1, 0, −2, −2), (2, 1, 1, − 1)
(1, 1, 1, 1), (1, 2, 1, 0), (1, 3, 0, 0)
In Exercises 23 and 24, use f. g
18.
-2
[10] [oo]
n = 1, 2,
20. (1, 1, 0, 0), (0, 1, 1, 0), (1, 0, 1, 1)
= $₁,50
f₁(x) = 1, f₂(x) = x, f3(x) = x²
g₁(x) = 1 - x, g₂(x) = 1 + x, g3(x) = 1 + x + x²
In Exercises 27 and 28, use f. g
In Exercises 25 and 26, use A B = a₁₁b₁₁ + a₁2b₁2 + a21b₂1 + a2222-
●
11
636363
f(x)g (x) dx.
26.
(2π
Lo
f(x)g (x) dx and let f(x) = sin(nx),
Show that fn fm = 0 if n‡m. (HINT Use the identity sin u sin v =
[cos(u - v) - cos(u + v)].)
28. Compute ||f|| and produce an infinite collection of orthonormal "vectors."
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