1. ## 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?

2. 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 we have the following example.

Not sure if this helps.

3. Thanks for the response! Appreciate your help.