We define a homogeneous linear system and express a solution to a system of equations as a sum of a particular solution and the general solution to the associated homogeneous system.https://ximera.osu.edu/la/LinearAlgebra/SYS-M-0050/main
We define closure under addition and scalar multiplication, and we demonstrate how to determine whether a subset of vectors in R^n is a subspace of R^n.https://ximera.osu.edu/la/LinearAlgebra/VSP-M-0020/main
We define bases and consider examples of bases of Rn and subspaces of Rn.https://ximera.osu.edu/la/LinearAlgebra/VSP-M-0030/main
We discuss existence of bases of R^n and subspaces of R^n, and define dimension.https://ximera.osu.edu/la/LinearAlgebra/VSP-M-0035/main
We define the row space, the column space, and the null space of a matrix, and we prove the Rank-Nullity Theorem.https://ximera.osu.edu/la/LinearAlgebra/VSP-M-0040/main
We state the definition of an abstract vector space, and learn how to determine if a given set with two operations is a vector space. We define a subspace of a vector space and state the subspace test. We find linear combinations and span of elements of a vector space.https://ximera.osu.edu/la/LinearAlgebra/VSP-M-0050/main
We revisit the definitions of linear independence, bases, and dimension in the context of abstract vector spaces.https://ximera.osu.edu/la/LinearAlgebra/VSP-M-0060/main