what are the coordinates of a vector relative to a basis? why are the vectors e1,.,en called the standard basis vectors? how can one check whether or not a set of vectors form a basis?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.1: The Geometry And Algebra Of Vectors
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g.2 lineal algebra 

Please provide a clear, correct, and well explained solutioon for the following

what are the coordinates of a vector relative to a basis?
why are the vectors e1,.,en called the standard basis vectors?
how can one check whether or not a set of vectors form a basis?
Transcribed Image Text:what are the coordinates of a vector relative to a basis? why are the vectors e1,.,en called the standard basis vectors? how can one check whether or not a set of vectors form a basis?
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