Let V be the set of real-valued functions that are defined at each x in the interval (-∞, ∞). If f = f(x) and g = g(x) are two functions in V and k is any scalar, we define the operations of addition and scalar multiplication by W (f+g)(x) = f(x) + g(x), (kf)(x) = kf(x).
Let V be the set of real-valued functions that are defined at each x in the interval (-∞, ∞). If f = f(x) and g = g(x) are two functions in V and k is any scalar, we define the operations of addition and scalar multiplication by W (f+g)(x) = f(x) + g(x), (kf)(x) = kf(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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Transcribed Image Text:a. Let V be the set of real-valued functions that are defined at each x in the interval (-∞, ∞). If
f = f(x) and g = g(x) are two functions in V and k is any scalar, we define the operations of
addition and scalar multiplication by
(f+g)(x) = f(x) + g(x),
(kf)(x) = kf(x).
Verify the Vector Space Axioms for the given set of vectors.
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