Originally Posted by

**Mollier** Hi,

**problem:**

Consider the set of all those vectors in $\displaystyle \mathbb{C}^3$ each of whose coordinates is either 0 or 1. How many different basis does this set contain?

**attempt:**

The set I have to choose from has the following elements in it.

$\displaystyle \{(1,0,0),(0,1,0),(0,0,1),(1,1,0),(0,1,1),(1,0,1), (1,1,1)\}$.

I've excluded (0,0,0) as this is not part of any basis. More precisely I have

$\displaystyle 2^3-1$ elements in my set.

Now I want to pick three vectors out of a set of seven such that they are linearly independent..Any hints on this one?

Thanks.