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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:Quote:
Originally Posted by jm456
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 http://upload.wikimedia.org/math/4/3...8fc174381a.png we have the following example.
http://upload.wikimedia.org/math/3/f...6bf2b20ed2.png
Not sure if this helps.
Thanks for the response! Appreciate your help.