Given a vector space E, let (u)iel be a family of vectors in E. Let v EE, and assume that v = Eielu. Then the family (A)ier of scalars such that v = Ciel Aili is unique iff (u)iel is linearly independent.
Given a vector space E, let (u)iel be a family of vectors in E. Let v EE, and assume that v = Eielu. Then the family (A)ier of scalars such that v = Ciel Aili is unique iff (u)iel is linearly independent.
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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![Given a vector space E, let (u)iel be a family of vectors in E. Let v E E,
and assume that v = Zieliu. Then the family ()ier of scalars such that v = Ciel ui
is unique iff (ui)ier is linearly independent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2df4d651-a502-4e9a-93b2-a531f91b18ad%2Fb175f9b7-3815-46ba-8bfe-ed9e462646ed%2Fy1yuihd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given a vector space E, let (u)iel be a family of vectors in E. Let v E E,
and assume that v = Zieliu. Then the family ()ier of scalars such that v = Ciel ui
is unique iff (ui)ier is linearly independent.
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