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 $

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