Question: Determine all pairs among the functions 1,.x. cos x, sin x,ex, that are orthogonal with respect to the L2 inner product on [

Determine all pairs among the functions 1,.x. cos π x, sin π x,ex, that are orthogonal with respect to the L2 inner product on [ - 1, 1 ].

Step by Step Solution

★★★★★

3.33 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

1 is orthogonal to x cos x sin x x ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

952-M-L-A-E (1962).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Using elementary geometry and the definition of sin x, cos x, we can show that for every x R i) | sin x| ii) sin(-x) = - sin x. cos(-x) = cos x, iii) sin2 x + cos2 x = 1, cos x = 1 - 2 sin2 (x/2),...

Q:

The functions cos x and sin x are both unit vectors in C[-Ï, Ï] with inner product defined by (a) Show that cos x ¥ sin x. (b) Determine the value of ||cos x + sin x||2. = | f(x)g(x)dx

Q:

The functions in Exercises 912 form two pairs of inverse functions. Determine which functions are inverses of each other. Exercises 912 y = log 3 (x + 2) y = 5 - 2 x y = log 2 (5 - x) y = 3 x - 2 A....

Q:

SOLVE Questions 1-5: PLEASE AND THANK YOU 1: What is the difference between homogenous and non-homogenous differential equation? Write an example for each and solve it. 2: What is the main formula to...

Q:

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Q:

Using the L2 inner product on the interval [0, nr] find the angle between the functions (a) 1 and cos x (b) 1 and sin x (c) cos x and sin x

Q:

Least Squares Approximation Hector D. Ceniceros 1 Least Squares Approximation Let f be a continuous function on [a, b]. We would like to find the best approximation to f by a polynomial of degree at...

Q:

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Q:

Chapter 7.1 Write on paper for upvote. questions: 1, 3 , 5, 11, 12, 26 please -145 -1455 - 1450 H O O HIN O HIN -NO InNo -No (6) HIN #ND HID Into O O a. for every vector x in R". As a first step in...

Q:

Please answer all the required questions in detail I hope the answer is not copy-paste I hope that the answer will be according to the concepts in the chapter 3 The following article summarizes the...

Q:

24.a) Calculate the total tax on an income of $289,600 Taxable income $0 $50,001 $75,001 $100,001 $335,001 $50,000 $75,000 $100,000 $335,000 $10,000,000 Tax Rate 15% 25% 34% 39% 34%

Q:

Can process costing be used for a service organization? Explain. Explain how process costing can be used for JIT manufacturing firms.

Q:

Evaluate each of the following integrals by considering some simple geometric shape. ( a ) 0 3 | ? ? x ? ? | d x , ( Recall the floor function in Definition 1 . 3 9 ) ( b ) 0 4 ( 4 - | x - 1 | - | x...

Q:

What duties does apparent authority impose on principals?

Q:

Two masses are connected by springs as shown in the diagram. Both springs have the same spring constant, and the end of the first spring is fixed. If x1 and x2 represent the displacements from the...

Q:

In each of the following, factor the matrix A into a product XDX-1. where D is diagonal. a. b. c. d. e. f. 2 3 A=10 12 0 0-1 031 121 123

Q:

Let A he an n x n matrix with positive real cigenvalucs λ1 > λ2 >...... >λn. Let xi he an eigenvector belonging to λi, for each i, and let x = a1x1...

Q:

Problem : GPA ConverterIn the CSC 2 6 2 Course Outline, there is a Grade Table that shows the conversion from course grades in points to letter grades ( A , A - , B + , etc. ) and from letter grades...

Q:

Consider the following two assets: Asset A: expected return is 4% and standard deviation of return is 42% Asset B: expected return is 1.5% and standard deviation of return is 24% The correlation...

Q:

Northern Pacific Heating and Cooling Inc. has a 6-month backlog of orders for its patented solar heating system. To meet this demand, management plans to expand production capacity by 45% with a $5...