My professor says that a linearly independent subset of a vector space automatically spans the vector space, and that a subset of a vector space that spans the vector space is automatically linearly independent.(adsbygoogle = window.adsbygoogle || []).push({});

I don't understand why either of these is true.

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

Join Physics Forums Today!

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

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

# Span and Linear Independence

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