1. 4.3: Determinants and the Area of a triangle using a matrix
Objectives: Students will be able to…
Find the determinant of a 2x2 matrix and a 3.3 matrix
Find the area of a triangle on the coordinate plane using a matrix

2. Determinant A real number associated with a square matrix
Determinant for Matrix A denoted by det A or |A|
DETERMINANT FOR A 2 X 2 MATRIX:
ad – cb
(Difference of the products of the entries on the diagonals)

3. Example:
Evaluate the determinant for the matrix below.

4. Determinant for a 3 x 3 matrix
Rewrite the first 2 columns to the right of the determinant
Subtract the sum of the products in red from the products in blue.
a b
det d e
g h
= (aei + bfg + cdh) – (gec + hfa + idb)

5. Evaluate the determinant

6. Example

7. ± choose appropriate sign to yield a positive value
Area of a triangle
The area of a triangle with vertices (x1,y1), (x2,y2), and (x3,y3) is given by:
Area =
± choose appropriate sign to yield a positive value

8. Find the area of a triangle with the following vertices
(5, -2) (3, 3) (-4,1)

9. The cities of San Francisco (-30, 32), Oakland (-16,40), and San Jose (0,0) form a triangular shaped area. Estimate the area formed by the 3 cities.

10. To find determinant on calculator
Enter Matrix
Matrix MATH :det( Enter name of matrix

11. What is the difference between the following: