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Let f, g = P2 (R) and define (f, g) = f(0)g(0). Select all the conditions which (...) do not met, or else conclude that (,) is an inner product on P₂ (R). Select all correct options. (f,g): (g, f) for every f, g = P₂ (R) (f+g,h) = (f,h) + (g, h) for every f, g, h = P₂ (R) (Af, g) = X(f, g) for every f, g = P2 (R) and A ER (f, f) ≥ 0 for every f = P2 (R) (f, f) = 0 if and only if f is the zero polynomial. (,) is an inner product on P2 (R)

Let f, g = P2 (R) and define (f, g) = f(0)g(0). Select all the conditions which (...) do not met, or else conclude that (,) is an inner product on P₂ (R). Select all correct options. (f,g): (g, f) for every f, g = P₂ (R) (f+g,h) = (f,h) + (g, h) for every f, g, h = P₂ (R) (Af, g) = X(f, g) for every f, g = P2 (R) and A ER (f, f) ≥ 0 for every f = P2 (R) (f, f) = 0 if and only if f is the zero polynomial. (,) is an inner product on P2 (R)

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 1E: Complete the proof of Theorem 5.30 by providing the following statements, where and are arbitrary...
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2 Let f, g = P₂ (R) and define (f,g) = f(0)g(0). Select all the conditions which (.,.) do not met, or else conclude that (.,.) is an inner product n P₂ (R). on Select all correct options. 0 0 0 0 0 0 (f,g) = (g, f) for every f, g = P₂ (R) (f+g, h) = (f, h) + (g, h) for every f, g, h = P₂ (R) (\f, g) = X(ƒ, g) for every f, g = P₂ (R) and λ = R (f, f) ≥ 0 for every f = P₂ (R) (f, f) (.,.) is an inner product on P₂ (R) - 0 if and only if f is the zero polynomial.
Transcribed Image Text:2 Let f, g = P₂ (R) and define (f,g) = f(0)g(0). Select all the conditions which (.,.) do not met, or else conclude that (.,.) is an inner product n P₂ (R). on Select all correct options. 0 0 0 0 0 0 (f,g) = (g, f) for every f, g = P₂ (R) (f+g, h) = (f, h) + (g, h) for every f, g, h = P₂ (R) (\f, g) = X(ƒ, g) for every f, g = P₂ (R) and λ = R (f, f) ≥ 0 for every f = P₂ (R) (f, f) (.,.) is an inner product on P₂ (R) - 0 if and only if f is the zero polynomial.
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