Let X be finite subset of a vector space V (spans V). Show that there is a subset of X which is a basis for V

Question

How would you go about doing this??

Thanks for any replies

Answer 1

Take the largest subset of X that's linearly independent.

It spans the rest of X (because of how we chose it), and hence all of V. On the other hand, it's linearly independent. So it's a basis.