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Math Help - Question on Spanning

  1. #1
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    Question on Spanning

    I am having a problem with a linear algebra concept. I thought in order for a set of vectors to span a vector space they had to be expressible as linear combinations, therefore, linerarly dependent. If this is true, how can the set of vectors that are a basis for a vector space by definition be both: 1) linearly independent and 2) span the vector space?
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  2. #2
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    Quote Originally Posted by jm456 View Post
    I am having a problem with a linear algebra concept. I thought in order for a set of vectors to span a vector space they had to be expressible as linear combinations, therefore, linerarly dependent. If this is true, how can the set of vectors that are a basis for a vector space by definition be both: 1) linearly independent and 2) span the vector space?
    You might want to take a look at this link:
    Linear independence - Wikipedia, the free encyclopedia

    It is mentioned in there that:

    In linear algebra, a family of vectors is linearly independent if none of them can be written as a linear combination of finitely many other vectors in the collection. A family of vectors which is not linearly independent is called linearly dependent. For instance, in the three-dimensional real vector space we have the following example.


    Not sure if this helps.
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  3. #3
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    Thanks for the response! Appreciate your help.
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