Use the inner product in the vector space of continuous functions Use the inner product1(f,g) = / f(x)g(x) dxin the vector space C°[0, 1] of continuous functions on the domain [0, 1] to find (f, g), ||f ||, ||g|| forf(x) = -5x2 – 6 and g(x) = 6x + 1.(f, 8) =I|f|| =llg|| =

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Use the inner product 1 (f, 8) = f(x)g(x) dx in the vector space CO[0, 1] of continuous functions on the domain [0, 1] to find (f, g), ||f ||, ||g|| for f(x) = -5x² – 6 and g(x) = 6x + 1. %D (f,g) = ||S|| = lg| :

Use the inner product 1 (f, 8) = f(x)g(x) dx in the vector space CO[0, 1] of continuous functions on the domain [0, 1] to find (f, g), ||f ||, ||g|| for f(x) = -5x² – 6 and g(x) = 6x + 1. %D (f,g) = ||S|| = lg| :

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}

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Question

Use the inner product in the vector space of continuous functions

Use the inner product
1
(f,g) = / f(x)g(x) dx
in the vector space C°[0, 1] of continuous functions on the domain [0, 1] to find (f, g), ||f ||, ||g|| for
f(x) = -5x2 – 6 and g(x) = 6x + 1.
(f, 8) =
I|f|| =
llg|| =

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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