Systems of Linear Equations
- writing systems of equations as matrix multiplication
- a particular solution vs the solution set
- consistent system of equations (has at least one solution)
- inconsistent system of equations (no solution)
- geometric interpretation

Geometry
- vector equation of a line (one parameter)
- vector equation of a plane (two parameters)
- vector equation of a hyperplane (more than 2 parameters)

Solving systems of equations
- augmented matrix
- row operations (on a matrix)

- equivalent systems of equations
- row echelon form RE
- Gaussian Elimination
- reduced row echelon form RRE
- Gauss-Jordan Elimination

- row equivalent matrices
- coefficient matrix
- rank of a matrix (rk(A))
- relation of rank to solutions of equations
- homogeneous system of equations (Ax=0)
- associated homogeneous system of equations ( Ax=B has associated system Ax=0 )

- elementary matrices
- If E is an elementary matrix then EA is the matrix A with the row operation of E done to it

- relationship between rk(A), A inverse, RRE form of A, solutions to Ax=0

Vector Spaces

-subspaces
-linear combination
-span{v1,v2,...,vn}
-linearly dependent set of vectors
-linearly independent set of vectors
-spanning set (for a subspace)
-basis
-dimension

-Col(A),Row(A),Null(A) and finding their bases and dimensions
-dim(Null(A))+dim(Col(A))=m where A is n x m matrix