True or False: P-Dimensional Subspace and Basis for R^n

[Dwolfson]

Homework Statement

If H is a p-dimensional subsapce for R^n and {v₁,...v_p}
is a spanning set of H, then {v₁,...v_p} is automatically a basis for H.


True or False

Homework Equations

I am unsure of my answer.

The Attempt at a Solution

I am under the impression that this is true due to the fact that since the subspace is p-dimensional that {v₁,...v_p} is a basis because it must be linearly independent because this set spans p-dimensions thus needs p vectors.

 

[Mark44]

That's pretty much it. If you have p vectors that are linearly independent, and that span a subspace of dimension p, then these vectors are a basis for that subspace.