1. Definition of Cofactors
Determinants
Definition of Cofactors

2. Definition of Cofactors
Let M =
The cofactor of the i-th row and the j-th column is defined by
Aij = (-1)i + j(2 x 2 determinant obtained by deleting the i-th row and the j-th column)

3. Definition of Cofactors
Let M =
The cofactor of the i-th row and the j-th column is defined by
Aij = (-1)i + j(2 x 2 determinant obtained by deleting the i-th row and the j-th column)

4. Definition of Cofactors
Let M =
The cofactor of the i-th row and the j-th column is defined by
Aij = (-1)i + j(2 x 2 determinant obtained by deleting the i-th row and the j-th column)

5. Relation between Cofactors and Determinants
Let M =
det M = aei + bfg + cdh – ceg – afh – bdi
Expansion along the 1st row

6. Expansion along the 2nd row
Let M =
det M = aei + bfg + cdh – ceg – afh – bdi
Expansion along the 2nd row

7. Expansion along the columns
Expansion along the 1st column

8. Properties of Determinant

9. = bei +bfh +ceh
- ceh – bei - bfh
= 0

10. Expansion along the columns
Expansion along the 1st column
What should be the value of
bA11 + eA21 + hA31? e h b
= 0
Similarly, aA21 + bA22 + cA23 = 0.

11. Why?

12. Expansion along the columns
Expansion along the 1st column
What should be the value?
How about
Ans: k3detA

13. What is the value of
= 0

14. If
Then what is the value of
= ?
Ans: 0

15. Applications = (a + a’)A11 + (d + d’)A21 + (g + g’)A31
= (aA11 + dA21 + gA31) + (a’A11 + d’A21 + g’A31)
Why?

16. Why?

17. Examples:
= 80

18. = -67

19. The End.