Answered: iii. Does there exist a function x e X… | bartleby

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 16CM

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Question

iii. Does there exist a function x E X such that
X(t) = t² +
e- F(s) ds
for every t e [0, 1]?
Justify your answer.

• Consider X = C[0, 1] with the norm
||x|| = max |x(t)\,
tE[0,1]
and let T : X → X be the mapping given by
(Tx)(1) = | e*x.
e-x(s) ds
for every t e [0, 1].

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