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### Episode 08a (31:02): "Paging Doctor Vector Spaceman"

#### Summary:

Time for a pragmatic introduction to vector spaces. We look at the definition of vector spaces, focusing on the big pieces and skating over the many hair-raising details. We describe what will be essential for all going forward: subspaces, vector spaces inside vector spaces. We go over some examples of sets that are subspaces and some that are not. Also: Doughnuts, apples, and rabbits.

#### Extra:

Coming soon: Column space, null space, and more. It's all about $\mathbf{A}\vec{x}=\vec{b}$.