Explanation Given: The set S is given by, S = { x : ‖ x ‖ = 1 } And the inner product is defined as, 〈 x , y 〉 = x T y . Approach: The norm of x is given as ‖ x ‖ = 〈 x , x 〉 . The general equation of circle having the center ( 0 , 0 ) and radius r is given by, x 2 + y 2 = r 2 . The general equation for an ellipse having the center ( 0 , 0 ) and the vertices ( a , 0 ) and ( 0 , − a ) is x 2 a 2 + y 2 b 2 = 1 . Calculation: Consider the inner product 〈 x , y 〉 = x T y Let, x = [ x 1 x 2 ] then the inner product 〈 x , x 〉 = x T x = [ x 1 x 2 ] T [ x 1 x 2 ] = [ x 1 x 2 ] [ x 1 x 2 ] = x 1 2 + x 2 2 The norm of x is given as ‖ x ‖ = 〈 x , x 〉 . Therefore, ‖ x ‖ = 〈 x , x 〉 = x 1 2 + x 2 2 Since, ‖ x ‖ = 1 Thus, from the above equation,

Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)

5th Edition

ISBN: 9780134689531

Author: Lee Johnson, Dean Riess, Jimmy Arnold

Publisher: PEARSON

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Chapter 5.6, Problem 13E

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To sketch:

The graph of S when 〈x,y〉=xTy, where S={x:‖x‖=1} and when the inner product defined in Exercise 1.

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Chapter 5.6, Problem 12E

Chapter 5.6, Problem 14E

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Chapter 5 Solutions

Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)

Ch. 5.2 - For u,v and w given in given Exercises 13,...Ch. 5.2 - For u,v and w given in given Exercises 13,...Ch. 5.2 - For u,v and w given in given Exercises 13,...Ch. 5.2 - Prob. 4E Ch. 5.2 - Prob. 5E Ch. 5.2 - In Exercises 6-11, the given set is a subset of a...Ch. 5.2 - Prob. 7E Ch. 5.2 - In Exercises 6-11, the given set is a subset of a...Ch. 5.2 - In Exercises 6-11, the given set is a subset of a...Ch. 5.2 - In Exercises 6-11, the given set is a subset of a...

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The graph of S when 〈 x , y 〉 = x T y , where S = { x : ‖ x ‖ = 1 } and when the inner product defined in Exercise 1.

Solution Summary: The author illustrates the graph of S when langle x,yrangle =xTy

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To sketch:

The graph of S when 〈x,y〉=xTy, where S={x:‖x‖=1} and when the inner product defined in Exercise 1.

Want to see the full answer?

Chapter 5 Solutions

The graph of S when 〈 x , y 〉 = x T y , where S = { x : ‖ x ‖ = 1 } and when the inner product defined in Exercise 1.

Solution Summary: The author illustrates the graph of S when langle x,yrangle =xTy

Videos

To sketch: The graph of S when 〈x,y〉=xTy, where S={x:‖x‖=1} and when the inner product defined in Exercise 1.

Want to see the full answer?

Chapter 5 Solutions

To sketch:

The graph of S when 〈x,y〉=xTy, where S={x:‖x‖=1} and when the inner product defined in Exercise 1.