Linear Algebra


	Linear Algebra



	Linear Equations
	Systems of Linear Equations
	Row Reduction, Echelon Form
	Vector Equations
	Matrix Equation (Ax = b)
	Linear System Solution Sets
	Traffic Flow Application
	Linear Independence
	Linear Transformation
	Onto, One-to-One
	Matrix Algebra
	Matrix Operations
	Inverse of Matrix
	Properties of Invertible Matrices
	Partitioned Matrices
	Matrix Factorizations
	Calculating Determinants
	Properties of Determinants
	Spaces
	Vector Spaces, Subspaces
	Null Spaces, Column Spaces, Linear Transformations
	Bases
	Dimensions of Vector Spaces
	Rank
	Eigen
	Eigenvalues, Eigenvectors