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10. Using Theorem 6.4. (Gram-Schmidt process) obtain an orthonormal basis 3 v} for span(S). Then verify that a Espan(S) can be written in the {0₁, 02,1 form and r = A I = (a) V = R³, S = {(1, 0, 1), (0, 1, 1), (1,3,3)}, and x = (1,1,2). (b) V M₂(R) (with Frobenius norm) S -1 27 k Σ(x, v.)vi. i=1 3 -1 9 {G) (2) 6_D)} 5 -1 (c) V = span(S) with the inner product (f, g) = f(t)g(t) dt, S = {sin t, cost, t}, and h(t) = 2t + 1.

10. Using Theorem 6.4. (Gram-Schmidt process) obtain an orthonormal basis 3 v} for span(S). Then verify that a Espan(S) can be written in the {0₁, 02,1 form and r = A I = (a) V = R³, S = {(1, 0, 1), (0, 1, 1), (1,3,3)}, and x = (1,1,2). (b) V M₂(R) (with Frobenius norm) S -1 27 k Σ(x, v.)vi. i=1 3 -1 9 {G) (2) 6_D)} 5 -1 (c) V = span(S) with the inner product (f, g) = f(t)g(t) dt, S = {sin t, cost, t}, and h(t) = 2t + 1.

Advanced Engineering Mathematics
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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10. Using Theorem 6.4. (Gram-Schmidt process) obtain an orthonormal basis 3 v} for span(S). Then verify that a Espan(S) can be written in the {0₁, 02,1 form I = -1 27 k Σ(x, v.)vi. i=1 (a) V = R³, S = {(1, 0, 1), (0, 1, 1), (1,3,3)}, and x = (1,1,2). (b) V M₂(R) (with Frobenius norm) S and r = A (c) V = span(S) with the inner product (f, g) = f(t)g(t) dt, S = {sin t, cost, t}, and h(t) = 2t + 1. 3 -1 9 {G) (2) 6_D)} 5 -1
Transcribed Image Text:10. Using Theorem 6.4. (Gram-Schmidt process) obtain an orthonormal basis 3 v} for span(S). Then verify that a Espan(S) can be written in the {0₁, 02,1 form I = -1 27 k Σ(x, v.)vi. i=1 (a) V = R³, S = {(1, 0, 1), (0, 1, 1), (1,3,3)}, and x = (1,1,2). (b) V M₂(R) (with Frobenius norm) S and r = A (c) V = span(S) with the inner product (f, g) = f(t)g(t) dt, S = {sin t, cost, t}, and h(t) = 2t + 1. 3 -1 9 {G) (2) 6_D)} 5 -1
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