Class 3, Math 235 W08

Determinants (pdf file Sect 3.2, suppl. notes)

• Properties of determinant cont...:
  • det I=1; interchange rows changes sign; det is a linear function of row 1.
  • adding (a multiple of one row) to another row does not change det. (and other elementary row operations)
  • det A = 0 iff A is invertible/nonsingular (with proof using RREF)
  • properties of det allow one to use elementary row operations to get a triangular matrix and simplify calculation of det!!
  • A is invertible iff det A is nonzero
  • det A = det A^T