Is there a rule that number of vectors spanning $\mathbb{R}^n$ must be at least $n$?
For example, can three vectors span $\mathbb{R}^4$ ?
Is there a rule that number of vectors spanning $\mathbb{R}^n$ must be at least $n$?
For example, can three vectors span $\mathbb{R}^4$ ?
Yes. If a subset $S$ of $\mathbb{R}^n$ spans it, then $\#S\geqslant n$.