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, e2a}. When the the Gram-Schmidt process is applied to S, we obtain the orthogonal set S' = {1, e – e +1, v3 (x)}, where So f(t)g(t) dt for each f, g E V. Now, consider the linearly independent set vz (x) : e2a + a·1 + b· (eª e +1). Find the value of the number a. 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, e2a}. When the the Gram-Schmidt process is applied to S, we obtain the orthogonal set S' = {1, e – e +1, v3 (x)}, where So f(t)g(t) dt for each f, g E V. Now, consider the linearly independent set vz (x) : e2a + a·1 + b· (eª e +1). Find the value of the number a. 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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Question

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, e2a}. When the the Gram-Schmidt process is applied to S, we obtain the orthogonal set
S' = {1, e – e +1, v3 (x)}, where
So f(t)g(t) dt for each f, g E V. Now, consider the linearly independent set
vz (x) :
e2a + a·1 + b· (eª
e +1).
Find the value of the number a. Find the value of the number b.

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