If the elements v1 v2 ... vn form a basis for the vector space V, then the elements must span V and be linearly independant.
Also, the number of elements must be equal to the dimension of the vector space.
So my question is this:
If the number of elements is equal to the dimension of the vector space, and they are all linearly independant, will they always span V?
I feel pretty certain that they will, but I am not completely sure.
If they don't, what are some examples where they would not span but still be linearly independant?