Solution Found!
Prove the following infinite-dimensional version of Theorem 1.8 (p. 43): Let ft be a
Chapter 1, Problem 5(choose chapter or problem)
Prove the following infinite-dimensional version of Theorem 1.8 (p. 43): Let ft be a subset of an infinite-dimensional vector space V. Then ft is a basis for V if and only if for each nonzero vector v in V, there exist unique vectors u\, u2,..., un in ft and unique nonzero scalars C\, c 2 ,... , cn such that v ciui + c2u2 -\ 1- cnu
Questions & Answers
QUESTION:
Prove the following infinite-dimensional version of Theorem 1.8 (p. 43): Let ft be a subset of an infinite-dimensional vector space V. Then ft is a basis for V if and only if for each nonzero vector v in V, there exist unique vectors u\, u2,..., un in ft and unique nonzero scalars C\, c 2 ,... , cn such that v ciui + c2u2 -\ 1- cnu
ANSWER:Step 1 of 4
Suppose is the basis for and . Thus, it can be concluded that,
from
Hence, for vector linear combination is .