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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."

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 17E
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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."
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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