# Will any set containing n distinct vector in a n dimensional distinct vectors space be a spanning set?

Can any set of vector containing n vector in a n dimensional vector space be used to generate all other possible vectors in that vector space?

The answer is no. Consider the set $$\{(1,0),(2,0)\}$$ which is two distinct vectors in $\mathbb{R}^2$, and yet their span is not all of $\mathbb{R}^2$.