Question on Spanning

• Apr 11th 2009, 06:38 PM
jm456
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?
• Apr 11th 2009, 07:17 PM
knighty
Quote:

Originally Posted by jm456
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 http://upload.wikimedia.org/math/4/3...8fc174381a.png we have the following example.