1. Evaluate Determinants and Apply Cramer’s Rule
Notes 3.7 (Day 1)
Evaluate Determinants and Apply Cramer’s Rule

2. Finding the determinant of a 2 X 2 matrix.
The determinant of a 2 X 2 matrix is the product of the negatively sloped diagonal, minus the product of the positively sloped diagonal.

3. Find the determinant:

4. Find the determinant.

5. Finding the determinant of a 3 X 3 matrix.
Step 1: Repeat the first two columns to the right of the matrix.
Step 2: Take the sum of the product of the negatively sloped diagonals and subtract the sum of the positively sloped diagonals.

6. Find the determinant:

7. Find the determinant:

8. Directions: Solution: Step 1:Take the determinant of the matrix.
Find the area of a triangle with the vertices (x1, y1), (x2, y2), and (x3, y3).
Solution:
Step 1:Take the determinant of the matrix.
Step 2: Multiply the determinant by positive or negative one half.
This will be the area.

9. Example:
Find the area of the triangle with vertices A(5, 11), B(9, 2), and C(1, 3).

10. Example: Find the area of the triangle with vertices A(1, 5), B(4, 6),

11. Homework:
P , 22-27