2.57 † Let S = functions on [a,b]. Show that if n e N and if ao, a1,..., an are not all 0, then it is not possible for E-, aka* shows that C[a, b] is an infinite-dimensional vector space, because it cannot have finite dimension n for any n E N.) {1,x, x², x³, .}, a list of infinitely many continuous 0, the zero function. (Remark: This exercise k%3D0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
{1, x, x2, x,..., x",...}, a list of infinitely many continuous
2.57 † Let S
functions on [a,b]. Show that if n E N and if ao, a1,.
it is not possible for E-, akx* = 0, the zero function. (Remark: This exercise
shows that C[a, b] is an infinite-dimensional vector space, because it cannot have
finite dimension n for any n E N.)
..., An are not all 0, then
ian
Transcribed Image Text:{1, x, x2, x,..., x",...}, a list of infinitely many continuous 2.57 † Let S functions on [a,b]. Show that if n E N and if ao, a1,. it is not possible for E-, akx* = 0, the zero function. (Remark: This exercise shows that C[a, b] is an infinite-dimensional vector space, because it cannot have finite dimension n for any n E N.) ..., An are not all 0, then ian
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
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,