VectorSpaces.mws Vector Space Axioms Addition axioms: Scalar multiplication axioms: Definitions Span example: linear independence Basis example Subspaces Definition: example of a subspace of R^3; and more: The subspaces of R^2; and R^3;: Three more Subspaces e.g. E.R.O.'s and Row(A) and Col(A) e.g. consider the following matrices (this e.g. is from Anton): e.g. Find a basis for Row(A) in terms of the row vectors of A and express any vectors not in the basis as a linear combination of basis vectors if A is the following matrix. Another basis e.g. Rank and Nullity Final BIG statement of the course: Amen.