Can n Vectors in Rm Span All of Rm?

[MustangGt94]

Not sure if this is "beyond" Calculus but the prereq for the class was Calc II so I thought i'd post here.

Homework Statement

Could a set of n vectors in Rm span all of Rm?

Homework Equations

None

The Attempt at a Solution

Hmm really stuck at this one. I think that it should be able to span since the only thing that matters is if you have a pivot point in each column? So even if you have say 3 vectors in R4 it could still span it, since you can have still have a pivot point in each of the column if the vectors allow it?

Thanks for the help.

 

[Dick]

n<m, right? Can one vector span R2? Why or why not?