Basis is finite set of vectors that are linearly independant

[squenshl]

I know that the basis is finite set of vectors that are linearly independant and SPANS that set. But why is when you find the basis for the row space for example the answer is {[u1,u2,...,um}} and not span{[u1,u2,...,um}]. I got this wrong in a test. I don't see why eventhough the definition states that it spans that set.

 

[Hurkyl]

If {u1, u2, ..., um} spans the vector space V, then span{u1, u2, ..., um} = V, right? And V is obviously not a basis for V.

 

[HallsofIvy]

A basis is a set of vectors. The span of a set of vectors is a vector space, not a basis.