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Consider the operator Î = k, where k is a scalar, operating in a function space on the interval [a, b] with inner product defined by (f\g) = [°* f*(x)g(x)dx. a) Show that I is a linear operator, i.e., that is satisfies the necessary requirement for linear operators.

Consider the operator Î = k, where k is a scalar, operating in a function space on the interval [a, b] with inner product defined by (f\g) = [°* f*(x)g(x)dx. a) Show that I is a linear operator, i.e., that is satisfies the necessary requirement for linear operators.

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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Consider the operator Î = kd, where k is a scalar, operating in a function space on the interval [a, b] with inner product defined by dx' (f\g) = [°* f*(x)g(x)dx. a) Show that I is a linear operator, i.e., that is satisfies the necessary requirement for linear operators.
Transcribed Image Text:Consider the operator Î = kd, where k is a scalar, operating in a function space on the interval [a, b] with inner product defined by dx' (f\g) = [°* f*(x)g(x)dx. a) Show that I is a linear operator, i.e., that is satisfies the necessary requirement for linear operators.
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