Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
3. Let V denote the vector space of all functions f: R" → R, equipped with addition + : V x V → V defined via (f+g)(x) = f(x) + g(x), x = R", and scalar multiplication : Rx V → V defined via (X. f)(x) = \f(x), xER". Now let W = {f: R" → R: f(x) = ax + b for some a, b E R}, i.e. the space of all linear functions R" → R. (a) Show that W is a subspace of V. (You may assume that V is a vector space).

3. Let V denote the vector space of all functions f: R" → R, equipped with addition + : V x V → V defined via (f+g)(x) = f(x) + g(x), x = R", and scalar multiplication : Rx V → V defined via (X. f)(x) = \f(x), xER". Now let W = {f: R" → R: f(x) = ax + b for some a, b E R}, i.e. the space of all linear functions R" → R. (a) Show that W is a subspace of V. (You may assume that V is a vector space).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
3. Let V denote the vector space of all functions ƒ : R" → R, equipped with addition +: V × V → V defined via (ƒ+g)(x) = ƒ(x)+g(x), x = R", and scalar multiplication · : R × V → V defined via (λ · ƒ)(x) = \ƒ(x), x ER". Now let W = {ƒ {f: : Rª → R : ƒ(x) = ax + b for some a, b € R}, i.e. the space of all linear functions R" → R. (a) Show that W is a subspace of V. (You may assume that V is a vector space).
Transcribed Image Text:3. Let V denote the vector space of all functions ƒ : R" → R, equipped with addition +: V × V → V defined via (ƒ+g)(x) = ƒ(x)+g(x), x = R", and scalar multiplication · : R × V → V defined via (λ · ƒ)(x) = \ƒ(x), x ER". Now let W = {ƒ {f: : Rª → R : ƒ(x) = ax + b for some a, b € R}, i.e. the space of all linear functions R" → R. (a) Show that W is a subspace of V. (You may assume that V is a vector space).
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS