Prove :Let V be a vector space and ß = {x1,...,xn} be a subset of V. Then ß is a basis for V if and only if each vector y in V can be uniquely expressed as a linear combination of vectors in ß, i.e., can be expressed in the form y=a1x1 + ... +anxn, for unique scalars a1 ...,. an
Prove :Let V be a vector space and ß = {x1,...,xn} be a subset of V. Then ß is a basis for V if and only if each vector y in V can be uniquely expressed as a linear combination of vectors in ß, i.e., can be expressed in the form y=a1x1 + ... +anxn, for unique scalars a1 ...,. an
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.1: Orthogonality In Rn
Problem 7EQ
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Prove :
Let V be a vector space and ß = {x1,...,xn} be a subset of V. Then ß is a basis for V if and only if each vector y in V can be uniquely expressed as a linear combination of
y=a1x1 + ... +anxn,
for unique scalars a1 ...,. an
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