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1. 8.5 Applications of
Matrices and
Determinants
Objective: Use Cramer's rule to solve a
system of equations, find area of
triangles, and determine if three points
are collinear.
Standard: Linear Algebra 10.0

2. Methods for finding
determinants:
method 1: ______________
method 2: ______________
method 3: ______________

3. How are determinants used?

4. Cramer's Rule

5. Ex 1) Solve this system with Cramer's Rule.

6. Triangle Area:
Given 3 points, how can we find the area?

7. Ex. 2) Find the area of the triangle formed
by the points (0, 0), (4, 1), and (2, 5).

8. Ex. 2) Find the area of the triangle formed
by the points (0, 0), (4, 1), and (2, 5).

9. Collinear Points
What if the area of a triangle is 0?

10. Ex. 3) Are the points (3, –1), (0, –3), and
(9, 3) collinear?

11. Bonus!! Equation of a line!
Ex. 4) Find an equation through the points
(–4, 3) and (2, 1).