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(a) Let B = {V₁, V2, ..., Vn} be a basis for a finite-dimensional vector space V. Prove that for every n v € V there exists a unique choice of scalars C₁, C₂, ..., Cn such that v = Σcivi. i=1

(a) Let B = {V₁, V2, ..., Vn} be a basis for a finite-dimensional vector space V. Prove that for every n v € V there exists a unique choice of scalars C₁, C₂, ..., Cn such that v = Σcivi. i=1

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 33EQ
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(a) Let B = {V₁, V2, ..., Vn} be a basis for a finite-dimensional vector space V. Prove that for every n VE V there exists a unique choice of scalars C₁, C2, ..., Cn such that v = ΣCivi. i=1
Transcribed Image Text:(a) Let B = {V₁, V2, ..., Vn} be a basis for a finite-dimensional vector space V. Prove that for every n VE V there exists a unique choice of scalars C₁, C2, ..., Cn such that v = ΣCivi. i=1
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