(c) Consider R² with the norm ||x|| = |Eil + 1621 for any x = (E1,52) E R.Let y = (1, 1) e R? and find a linear functional f which has norm 1 and satisfiesfly) = llyll. Justify your answer.%3D

Answered: Image /qna-images/answer/e432019c-2e7a-4a59-ad9a-62420e3761c7.jpg

Answered: (c) Consider R? with the norm ||x|| =…

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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Use the Wronskian to determine if the given functions are linearly independent on the indicated interval. f(x) = 29, g(x) = 4x, h(x) = 2x²; the real line Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer.) A. The Wronskian W(f, g, h) = B. The Wronskian W(f, g, h) = OC. The Wronskian W(f, g, h) =| OD. The Wronskian W(f, g, h) = .As W is never 0 on the real line f(x), g(x) and h(x) are linearly independent. As W is identically 0 on the real line f(x), g(x) and h(x) are linearly independent. As W is identically 0 on the real line f(x), g(x) and h(x) are linearly dependent. As W is never 0 on the real line f(x), g(x) and h(x) are linearly dependent.
Use the Wronskian to determine if the given functions are linearly independent on the indicated interval. f(x) = 13, g(x)=x, h(x) = 3x²; the real line Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer.) OA. The Wronskian W(f, g, h) =. As W is identically 0 on the real line f(x), g(x) and h(x) are linearly dependent. OB. The Wronskian W(f, g, h) = C. The Wronskian W(f, g, h) = D. The Wronskian W(f, g, h) = . As W is never 0 on the real line f(x), g(x) and h(x) are linearly dependent. As W is identically 0 on the real line f(x), g(x) and h(x) are linearly independent. As W is never 0 on the real line f(x), g(x) and h(x) are linearly independent.
The Wronskian has been computed. Determine whether the functions are linearly independent or dependent. W = et %3D 2e* = 2e 2x - 2e2x = 0 et 2e* %3D O independent O dependent 98

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(c) Consider R? with the norm ||x|| = |Eil + 1E2| for any x = (Ei,52) E R.. Let y = (1, 1) € R? and find a linear functional f which has norm 1 and satisfies fly) = llyll. Justify your answer. %3D %3D