Finding basis of the subspace

Question

While finding the basis of a subspace in $\mathbb{R}^n$, is there a condition for the number of vectors or number of elements in the vectors? To be a subspace of $\mathbb{R}^n$, do you at least need $n$ number of vectors?

Answer 1

To be a subspace of R^n, do you at least need n number of vectors?

No. Take our familiar $\mathbb{R}^3$. A line (through the origin) is a one dimensional subspace. So you can span it by one suitable vector. Similar a plane (through the origin) by two suitable vectors.

Answer 2

It's the opposite: a basis of a subspace $V$ of $\mathbb{R}^n$ has at most $n$ vectors (and it has exactly $n$ vectors when and only when $V=\mathbb{R}^n$).