3.7 Determinants and Cramer’s Rule

1. 3.7 Determinants and Cramer’s Rule Determinants 1. Abbreviation form = det A. 2. Only work when the matrix is in a square form – nxn. 3. The value of determinant can be positive, negative, or zero. 4. If the value of determinant equals zero, then the inverse doesn’t exist – no solution. 5. Determinant will show if there is a solution or not.

2. Determinant of 2x2 Ex. Find the determinant of A.

3. Determinant of 3x3 Note: this procedures will work with 4x4, 5x5 and so on.

4. Ex. Find the determinant of A.

5. Finding the area of a triangle by applying the determinant. (x1,y1) (x2,y2) (x3,y3)

6. Ex. Finding the area of a triangle by applying the determinant. (0,2) (3,0) (0, – 2)

7. Cramer’s Rule for 2x2 1. det A ≠ 0. 2. 2x2 system where 3. The solution is and

8. Ex. Solve the system of linear equation by Cramer’s Rule.

9. Cramer’s Rule for 3x3 1. det A ≠ 0. 2. 3x3 system where 3. The solution is , and Note: The procedures are the same with 5x5, 6x6 and so on.