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P-Dimensional Subspace

1. The problem statement, all variables and given/known data

If H is a p-dimensional subsapce for R^n and {v1,...vp}
is a spanning set of H, then {v1,...vp} is automatically a basis for H.True or False2. Relevant equations

I am unsure of my answer.

3. 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,...vp} is a basis because it must be linearly independent because this set spans p-dimensions thus needs p vectors.  

    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.
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