1. Suppose V is the vector space of continuous functions f: [-1, 1] → R (a Show that (,): V × V → R given by defines an inner product. (f,g) = [² f(x)g(x)(1 − x²) da dx 1
1. Suppose V is the vector space of continuous functions f: [-1, 1] → R (a Show that (,): V × V → R given by defines an inner product. (f,g) = [² f(x)g(x)(1 − x²) da dx 1
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...
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![1. Suppose V is the vector space of continuous functions f: [-1, 1] → R.
(a Show that (,): V × V → R given by
defines an inner product.
1
(f,g) = [', f(x)g(a)(1 − a²) da
-1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3bf94c32-1ae7-46f0-be55-c39528493b25%2Fc1a56206-723e-4b11-9891-5bb31841b6c7%2Fqpc7v0mi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Suppose V is the vector space of continuous functions f: [-1, 1] → R.
(a Show that (,): V × V → R given by
defines an inner product.
1
(f,g) = [', f(x)g(a)(1 − a²) da
-1
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