(ii) Calculate the value of ||q|| (with respect to the given inner product).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 59E
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Q1(b)

1. Suppose V is the vector space of continuous functions ƒ : [−1, 1] → R.
(a) Show that (., .) : V × V → R given by
defines an inner product.
(f.9) = [ª f(x)g(x)(1 − x²) da
dx
1
Let p(x) 1 and g(x)
=
= x be elements of V.
(i) Calculate the value of ||p|| (with respect to the given inner product).
(ii) Calculate the value of ||q|| (with respect to the given inner product).
(iii) Calculate the angle between p and q (with respect to the given inner product).
Transcribed Image Text:1. Suppose V is the vector space of continuous functions ƒ : [−1, 1] → R. (a) Show that (., .) : V × V → R given by defines an inner product. (f.9) = [ª f(x)g(x)(1 − x²) da dx 1 Let p(x) 1 and g(x) = = x be elements of V. (i) Calculate the value of ||p|| (with respect to the given inner product). (ii) Calculate the value of ||q|| (with respect to the given inner product). (iii) Calculate the angle between p and q (with respect to the given inner product).
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