Linear Algebra › Section C · Determinants › Topic C.1

Determinants and cofactor expansion

Every square matrix carries a single number, its determinant, that says at a glance whether the matrix can be inverted. This topic defines that number and shows how to compute it by expanding along any row or column.

In this topic

  • One number for a square matrix
  • The 2 x 2 determinant
  • Minors and cofactors
  • Cofactor expansion
  • Worked example: a 3 x 3 determinant
  • Worked example: let the zeros work
  • Triangular matrices
  • Sarrus's rule and the cost of expansion
  • A short history
  • Common mistakes to avoid
  • Key takeaways

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