The vector space

* Linear combinations

** Linear combinations: JunkCo

** Lights Out

* Span

*** Span: Attacking the authentication scheme

** Generators

** Standard generators

* Geometry of sets of vectors: span of vectors over R

* Geometry of sets of vectors: Two representations

** Two representations: What's common?

* Abstract vector spaces

* Geometric objects that exclude the origin

** Affine space

*** Affine space and affine combination

*** Geometric objects not containing the origin: equations

*** The solution set of a linear system is either empty or an affine space

**** Number of solutions to a linear system

* Geometry of sets of vectors: convex hull

* 
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