This document discusses methods for solving systems of linear equations, including determinants of 3x3 matrices, cofactors, minors, adjugate matrices, inverses, and Cramer's rule. It provides examples of calculating determinants, finding the inverse and adjugate of a matrix, and using Cramer's rule to solve a system of equations. Cramer's rule allows solving systems when the determinant of the coefficients is not zero or when it is zero but the minor determinants are also zero, resulting in infinite solutions.

3. DETERMINANT OF ORDER 3X3

4. MINOR

5. CO-FACTORS
CO-FACTOR
MATRIX

6. EXAMPLE

8. ADJOINT & INVERSE OF A MATRIX

9. STEPS TO FIND INVERSE OF A
MATIX

11. SOLUTION OF SYSTEM OF LINEAR EQUATIONS

12. CRAMER’S RULE

13. STEPS: CRAMER’S RULE
Note that
D,D1,D2,D3 are
given as

14. EXAMPLE

15. (i)If D=0, then we check if any of D1, D2 or D3 is not zero then system is
inconsistent (ii)system is consistent with infinitely many solutions if
D1=D2=D3=0 along with D=0
(iii) In case (ii) above we replace any one variable by a constant k and proceed
in two variables only

16. THANK YOU