(0:02) Column echelon form, row-column duality.
(0:10) Cramer's Rule example.
(0:16) Example Continued.
(0:23) Multilinearity of the Determinant.
(0:36) Vector spaces: Solutions to systems with 3 variables.
(0:41) Planes: implicit description.
(0:44, 1:10) Planes: explicit description; vectors span the plane.
(0:49) Spanning diagrams.
(0:51) Plane through the origin is a vector space.
(0:57) All of 3-space as a linear combination of vectors.
