# Subspaces are the Natural Subsets of Linear Algebra | Definition + First Examples

A subspace is a subset that respects the two basic operations of linear algebra: vector addition and scalar multiplication. We say they are “closed under vector addition” and “closed under scalar multiplication”. On a subspace, you can do linear algebra! Indeed, a subspace is an example of a vector space. We see that all of R^n, {0}, and lines through the origin are all subspaces, but that lines NOT through the origin are not subspaces.

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