1. 5.4 Third Order Determinants and Cramer’s Rule

2. Third Order Determinants To solve a linear system in three variables, we can use third order determinants and Cramer’s Rule to do so. Definition: Third Order Determinant

3. An easier way to remember this is to copy the first two columns after the third column as shown. and we add the products of the first three diagonals going from the left and subtract the products of the first three diagonals going from the left. down up

4. Evaluate the determinant. 1.

5. Evaluate the determinant. 2.

6. Cramer’s Rule for 3 Variables for the system of equations

8. find that, if, the system has the unique solution If, then it means one of two things: 1. If and at least one of the determinants in the numerator is zero, then the system is inconsistent and there is no solution. 2. If and all the determinants in the numerators are, then the equations in the system are dependent and there are infinitely many solutions. not zero

9. Use Cramer’s Rule to solve the system. 3.

10. Use Cramer’s Rule to solve the system. 4.