Let V = C([0, 1]) (the set of all real, continuous functions with domain [0, 1]), and give V the inner product defined by (f, g) S = {1, eª , e2¤}. When the the Gram-Schmidt process is applied to S, we obtain the orthogonal set S' = {1, e² – e +1, v3(x)}, where So f(t)g(t) dt for each f, g € V. Now, consider the linearly independent set %3D v3 (x) = e2a + a·1 + b· (eª – e + 1). Find the value of the number b.
Let V = C([0, 1]) (the set of all real, continuous functions with domain [0, 1]), and give V the inner product defined by (f, g) S = {1, eª , e2¤}. When the the Gram-Schmidt process is applied to S, we obtain the orthogonal set S' = {1, e² – e +1, v3(x)}, where So f(t)g(t) dt for each f, g € V. Now, consider the linearly independent set %3D v3 (x) = e2a + a·1 + b· (eª – e + 1). Find the value of the number b.
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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![Let V = C([0, 1]) (the set of all real, continuous functions with domain [0, 1]), and give V the inner product
defined by (f, g)
S = {1, e¤, e2a}. When the the Gram-Schmidt process is applied to S, we obtain the orthogonal set
S' = {1, e² –
S f(t)g(t) dt for each f, g E V. Now, consider the linearly independent set
e +1, v3(x)}, where
V3 (x) = e2" + a ·1 + b. (e* – e +1).
Find the value of the number b.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fdefaca-e517-410c-b2a6-6a28c51deca0%2F5259e4f9-20bf-4d7d-a5fe-f97d9111d8c5%2F1ooh5x8_processed.png&w=3840&q=75)
Transcribed Image Text:Let V = C([0, 1]) (the set of all real, continuous functions with domain [0, 1]), and give V the inner product
defined by (f, g)
S = {1, e¤, e2a}. When the the Gram-Schmidt process is applied to S, we obtain the orthogonal set
S' = {1, e² –
S f(t)g(t) dt for each f, g E V. Now, consider the linearly independent set
e +1, v3(x)}, where
V3 (x) = e2" + a ·1 + b. (e* – e +1).
Find the value of the number b.
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