I can't seem to figure this one out:(adsbygoogle = window.adsbygoogle || []).push({});

Question: Let D be a nonempty subset of a vector space V over a field F. Let B be a finite linearly independet subset of span D having n elements. Prove there exists a subset D' of D also having n elements such that

span[(D-D') U B] = span(D).

Moreover, if D is linearly independent, so is (D-D') U B.

Can anyone help?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Spanning sets

**Physics Forums | Science Articles, Homework Help, Discussion**