Linear Dependence and Spans - A First Course in Linear Algebra


In any linearly dependent set there is always one vector that can be written as a linear combination of the others. This is the substance of the upcoming Theorem DLDS. Perhaps this will explain the use of the word “dependent.” In a linearly dependent set, at least one vector “depends” on the others (via a linear combination).

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GFDL-1.2
Submitted At
September 11th, 2017
 3 years ago
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 Textbook
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 English
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  • Theorem: a set of vectors is linearly dependent if and only if one of the vectors can be written as a linear combination of the other vectors, coordinate vector space. math.la.t.vec.lindep.coord

History

September 11th, 2017 3 years ago

Submitted by Jim Fowler