Determinants

Determinants

1. Determinant of 2 x 2 matrix

2. 3 x 3 Matrix or Greater

   • ij-th sign
   • ij-th minor
   • ij-th cofactor
   • Laplace Expansion

3. Special Cases

   • Triangular Matrix
     • Its Determinant
     • Upper vs Lower Triangular
   • Row/Column of Zeroes or 2 Rows that are Multiples

4. Effects of EROs on the Determinant

   • S: switching 2 Rows
   • M: multiplying row by scalar
   • A: adding multiple of row to another row
   • Analogous Theorem for ECOs

5. Cramer's Rule

6. Polynomial Interpolation

7. Rules

   • The Determinant of kA
   • Inverses
     • The Determinant of an Invertible Matrix can/cannot be...
     • The Determinant of the Inverse Matrix
   • The Determinant of the Transpose Matrix
   • The Determinant of AB
   • The Determinant of the Power of a Matrix

8. The Cofactor Matrix and The Adjugate

   • The Cofactor Matrix
   • The Adjugate
   • The Adjugate Formula and its Derivation