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# Pc 8.5 notes_appsof_det

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### Pc 8.5 notes_appsof_det

1. 1. 8.5 Applications ofMatrices andDeterminantsObjective: Use Cramers rule to solve asystem of equations, ﬁnd area oftriangles, and determine if three pointsare collinear.Standard: Linear Algebra 10.0
2. 2. Methods for ﬁndingdeterminants:method 1: ______________method 2: ______________method 3: ______________
3. 3. How are determinants used?
4. 4. Cramers Rule
5. 5. Ex 1) Solve this system with Cramers Rule.
6. 6. Triangle Area:Given 3 points, how can we ﬁnd the area?
7. 7. Ex. 2) Find the area of the triangle formedby the points (0, 0), (4, 1), and (2, 5).
8. 8. Ex. 2) Find the area of the triangle formedby the points (0, 0), (4, 1), and (2, 5).
9. 9. Collinear Points What if the area of a triangle is 0?
10. 10. Ex. 3) Are the points (3, –1), (0, –3), and(9, 3) collinear?
11. 11. Bonus!! Equation of a line!Ex. 4) Find an equation through the points(–4, 3) and (2, 1).