How would I prove this theorem:(adsbygoogle = window.adsbygoogle || []).push({});

"The column space of an m x n matrix A is a subspace of R^m"

by using this definition: A subspace of a vector space V is a subset H of V that has three properties: a) the zero vector of V is in H. b) H is closed under vector addition. c) H is closed under multiplication by scalars.

Please help

**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!

# Column space

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