1. DETERMINA NT

2. Adjoint Matrix – Minors and Cofactors  The adjoint matrix of [A], Adj[A] is obtained by taking the transpose of the cofactor matrix of [A].

3. Consider the following linear equation: Transform the linear system into coefficient matrix:

4. Determinant of a matrix using the Minors and Cofactors

5. Example: Find the Determinant of the matrix using the cofactor theorem 21 14 =8 - 1 = 7 a 11 = 1 a 12 = 2 a 13 = 3 C 11 = 7 C 12 = 5 C 13 = -4

6. Determinant of A = -15 ElementMinor CofactorElement x Cofactor a 11 = 177 a 12 = 2-5-10 a 13 = 3-4-12 a 11 a 12 a 13 +-+ 7 + (-10) + (-12) = -15