# Could a set of n verctors in Rm span all of Rm when n<m?

## Main Question or Discussion Point

Could a set of n verctors in Rm span all of Rm when n<m?
any hits? kinda confused with this span thing.

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matt grime
Homework Helper
R^m is m dimensional real space (it is easy to write down m independent vectors that span).

Just look at the definitions: the dimension is the minimal cardinality of a spanning set.

mathwonk
Homework Helper
you still have to prove that less than nvectors cannot span R^n.

i.e. you have to prove that the space of n tuples of real numbers has dimension n.

look at my web notes on linear algebra.

HallsofIvy
Homework Helper
Unfortunately, Yooyo did not give any indication as to what he had tried and so we have no idea what facts he can use!

Yooyo, back to you! Are you allowed to use the fact that Rn has dimension n or is proving that part of your problem?

mathwonk
Homework Helper
can you prove one vector cannot spane R^2?

mathwonk