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
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
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