# Basis and Span

#### Yankel

##### Active member
Hello

A base of some space is a set of vectors which span the space, and are also linearly independent.

I am looking for an example of vectors which DO span some space, but are dependent and thus not a base...can anyone give me a simple example of such a case ?

thanks !

#### Jameson

For example, the vectors $$\displaystyle \left \{ (1,0),(0,1),(1,2) \right \}$$ span $\mathbb{R}^2$ but this set isn't a basis.