Chapter SLE  Systems of Linear Equations

We will motivate our study of linear algebra by studying solutions to systems of linear equations. While the focus of this chapter is on the practical matter of how to find, and describe, these solutions, we will also be setting ourselves up for more theoretical ideas that will appear later.

 Section WILA What is Linear Algebra?
  Subsection LA: “Linear” + “Algebra”
  Subsection AA: An Application
  Subsection READ: Reading Questions
  Subsection EXC: Exercises
  Subsection SOL: Solutions
 Section SSLE Solving Systems of Linear Equations
  Subsection SLE: Systems of Linear Equations
  Subsection PSS: Possibilities for Solution Sets
  Subsection ESEO: Equivalent Systems and Equation Operations
  Subsection READ: Reading Questions
  Subsection EXC: Exercises
  Subsection SOL: Solutions
 Section RREF Reduced Row-Echelon Form
  Subsection MVNSE: Matrix and Vector Notation for Systems of Equations
  Subsection RO: Row Operations
  Subsection RREF: Reduced Row-Echelon Form
  Subsection READ: Reading Questions
  Subsection EXC: Exercises
  Subsection SOL: Solutions
 Section TSS Types of Solution Sets
  Subsection CS: Consistent Systems
  Subsection FV: Free Variables
  Subsection READ: Reading Questions
  Subsection EXC: Exercises
  Subsection SOL: Solutions
 Section HSE Homogeneous Systems of Equations
  Subsection SHS: Solutions of Homogeneous Systems
  Subsection NSM: Null Space of a Matrix
  Subsection READ: Reading Questions
  Subsection EXC: Exercises
  Subsection SOL: Solutions
 Section NM Nonsingular Matrices
  Subsection NM: Nonsingular Matrices
  Subsection NSNM: Null Space of a Nonsingular Matrix
  Subsection READ: Reading Questions
  Subsection EXC: Exercises
  Subsection SOL: Solutions
  Annotated Acronyms SLE: Systems of Linear Equations