Question

Let Z be the vector space of all the continuous functions on [1, 2] and let $f, g \in Z$ such that the inner product on this space is defined as $(f, g) = \int_{1}^{2} f(x)g(x)dx$. Show whether it is a valid inner product.

Name: Let Z be the vector space of all the continuous functions on [1, 2] and let f, g ∈ Z such that the inner product on this space is defined as (f, g) = ∫1^2 f(x)g(x)dx. Show whether it is a valid inner product.
Uploaded: 2022-02-28T17:02:48-08:00
Duration: 8 min 1 s
Channel: Harbir S
Description: Let Z be the vector space of all the continuous functions on [1, 2] and let f, g ∈ Z such that the inner product on this space is defined as (f, g) = ∫1^2 f(x)g(x)dx. Show whether it is a valid inner product.

          Let Z be the vector space of all the continuous functions on [1, 2] and let $f, g \in Z$ such that the inner product on this space is defined as $(f, g) = \int_{1}^{2} f(x)g(x)dx$. Show whether it is a valid inner product.

Let Z be the vector space of all the continuous functions on [1, 2] and let f, g ∈ Z such that the inner product on this space is defined as (f, g) = ∫1^2 f(x)g(x)dx. Show whether it is a valid inner product.

Added by Jason A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Harbir S

02/28/2022

Step 1

The first property we need to check is linearity in the first argument. This means that for any functions f, g, and h in Z and any scalars a and b, the inner product should satisfy the following: - (:af + bg, h:) = a(:f, h:) + b(:g, h:) Show more…

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Let Z be the vector space of all the continuous functions on 1,2 and let f,ginZ such that the inner product on this space is defined as (:f,g:)=int_1^2 f(x)g(x)dx. Show whether it is a valid inner product. Let Z be the vector space of all the continuous functions on [1,2] and let f,g EZ such that the inner product