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Chapter D  Determinants

The determinant is a function that takes a square matrix as an input and produces a scalar as an output. So unlike a vector space, it is not an algebraic structure. However, it has many beneficial properties for studying vector spaces, matrices and systems of equations, so it is hard to ignore (though some have tried). While the properties of a determinant can be very useful, they are also complicated to prove.

 Section DM Determinant of a Matrix
  Subsection EM: Elementary Matrices
  Subsection DD: Definition of the Determinant
  Subsection CD: Computing Determinants
  Subsection READ: Reading Questions
  Subsection EXC: Exercises
  Subsection SOL: Solutions
 Section PDM Properties of Determinants of Matrices
  Subsection DRO: Determinants and Row Operations
  Subsection DROEM: Determinants, Row Operations, Elementary Matrices
  Subsection DNMMM: Determinants, Nonsingular Matrices, Matrix Multiplication
  Subsection READ: Reading Questions
  Subsection EXC: Exercises
  Subsection SOL: Solutions