# What is a "subspace" in linear algebra?

A subset (call it W) of vectors is a subspace when it satisfies these conditions:

Testing these conditions is the best way to see if W is a subspace.

Some common subspaces of ${\mathbb R}^3$

• The zero vector, $\vec 0$
• A line running through the origin
• A plane passing through the origin
• ${\mathbb R}^3$