Explanation Given: f , g , h are continuous on [ a , b ] and c is a real number. Calculation: f , g , h are continuous on [ a , b ] and c is a real number. An inner product of a function continuous real valued function is, ( f , g ) = ∫ a b f ( x ) g ( x ) d x … (1) Substitute f for g in Equation (1). ( f , f ) = ∫ a b f ( x ) f</ To determine (b) ( f , g ) = ( g , f ) To determine (c) ( f + h , g ) = ( f , g ) + ( g , h ) To determine (d) ( c f , g ) = c ( f , g )

Fundamentals of Differential Equations [With CDROM] - 7th Edition

7th Edition

ISBN: 9780321410481

Author: Saff, Edward B., Snider, Arthur David, Nagle, R. Kent

Publisher: Addison Wesley

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Chapter 11.3, Problem 12E

To determine

(a)

(f,f)≥0 and equals zero only when f=0.

To determine

(b)

(f,g)=(g,f)

To determine

(c)

(f+h,g)=(f,g)+(g,h)

To determine

(d)

(cf,g)=c(f,g)

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Chapter 11.3, Problem 11E

Chapter 11.3, Problem 14E

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Chapter 11 Solutions

Fundamentals of Differential Equations [With CDROM] - 7th Edition

Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 3E Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 7E Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 9E Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...

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(a) ( f , f ) ≥ 0 and equals zero only when f = 0 .

Solution Summary: The author explains that (f,f)ge 0 and equals zero only when

Videos

(a)

(f,f)≥0 and equals zero only when f=0.

(b)

(f,g)=(g,f)

(c)

(f+h,g)=(f,g)+(g,h)

(d)

(cf,g)=c(f,g)

Want to see the full answer?

Chapter 11 Solutions

(a) ( f , f ) ≥ 0 and equals zero only when f = 0 .

Solution Summary: The author explains that (f,f)ge 0 and equals zero only when

Videos

(a) (f,f)≥0 and equals zero only when f=0.

(b) (f,g)=(g,f)

(c) (f+h,g)=(f,g)+(g,h)

(d) (cf,g)=c(f,g)

Want to see the full answer?

Chapter 11 Solutions

(a)

(f,f)≥0 and equals zero only when f=0.

(b)

(f,g)=(g,f)

(c)

(f+h,g)=(f,g)+(g,h)

(d)

(cf,g)=c(f,g)