Question

On P3 there is an inner product ∫ 20 f (x)g(x)dx defined by f ? g. a. Compute the length of x in this inner product. b. What is the angle between x and 1 in this inner product? c. If f, g, h form an orthonormal basis for P3 in this inner product, what is ∫ 20 (f + g + h)^2dx? Why? (Compute it)

Name: on p3 there is an inner product 20 f xgxdx defined by f g a compute the length of x in this inner product b what is the angle between x and 1 in this inner product c if f g h form an orthono 32343
Uploaded: 2022-02-11T08:27:54-08:00
Duration: 2 min 22 s
Channel: Ahmad Reda
Description: on p3 there is an inner product 20 f xgxdx defined by f g a compute the length of x in this inner product b what is the angle between x and 1 in this inner product c if f g h form an orthono 32343

          On P3 there is an inner product ∫ 20 f (x)g(x)dx defined by f ? g.
a. Compute the length of x in this inner product.
b. What is the angle between x and 1 in this inner product?
c. If f, g, h form an orthonormal basis for P3 in this inner product, what is ∫ 20 (f + g + h)^2dx? Why? (Compute it)

Added by William G.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Ahmad Reda

02/11/2022

Step 1

To compute the length of x in this inner product, we use the formula for the length of a vector in an inner product space: ||x|| = √(x ? x). In this case, it becomes ||x|| = √(∫ 20 x^2 dx). Show more…

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On P3 there is an inner product ∫ 20 f (x)g(x)dx defined by f ? g. a. Compute the length of x in this inner product. b. What is the angle between x and 1 in this inner product? c. If f, g, h form an orthonormal basis for P3 in this inner product, what is ∫ 20 (f + g + h)^2dx? Why? (Compute it)