1. Matrices and Determinants
Section 4-4
Matrices and Determinants
Objective:
To evaluate the determinant of a 3 x 3 matrix.
To find the area of a triangle given the coordinates of its vertices.

2. Determinants
Only square matrices have determinants.

3. Second-Order Determinant
-40 – -77 37

4. Third-Order Determinant
Determinants of 3x3 matrices are called third-order determinants.
One method of evaluating third-order determinants is called expansion by minors.
The minor of an element is the determinant formed when the row and column containing the element are deleted.

5. Expansion of a Third-Order Determinant

6. Example 1 2(40 – 63) – 3(48 – -7) + 4(54 – -5) 2(-23) – 3(55) + 4(59)
-46 – 25

7. Third-Order Determinant
Another method for evaluating a third-order determinant is using diagonals.
In this method, you begin by writing the first two columns on the right side of the determinant.

8. Diagonals Method

9. Example 2

10. Area of Triangles

11. Example 3
Find the area of the triangle whose vertices are located at (3, -4), (5, 4), (-3, 2).

12. Assignment
4-4 pg 209 #11-26 all