Applications of Matrices and Determinents

1. The Area of a Triangle with vertices (x1, y1) (x2, y2) (x3, y3)

A= +/- 1/2

l x1 y1 1 l

l x2 y2 1 l

l x3 y3 1 l

Remember to make sure that you use the +/- sign to always make the answer come out as a positive number.

Three Points are collinear if and only if: l x1 y1 1 l

l x2 y2 1 l = 0

l x3 y3 1 l

Example: Find the area of a triangle with vertices: (3,1) (2,3) (1,0)

A=+/- 1/2 3+0+2=5

l 3 1 1 l 3 1

l 2 3 1 l 2 3 10-5=5 +/- 1/2 (5)=2.5

l 1 0 1 l 1 0

9+1+0=10

Tip: Solve as you would a regular 3x3 matrix and multiply by +/- 1/2 to get a positive outcome.

Cramers Rule

ax+by=e

cx+dy=f

Example: 4x-2y=10

3x-5y=11

l 10 -2 l -50-(-22) = -28

l 11 5 l -28/-14 = 2

x= l 4 -2 l

l 3 -5 l -20-(-6) = -14

Final Answer = (2,-1)

l 4 10 l

y= l 3 11 l 44-30 = 14/-14 = -1

-14

Tips: Solve all matrices by finding the determinant of each. (ad-bc)

Since the numbers in the denominator are the same, the determinant does not change, therefore we don't need to solve it again.

For more help and tips please visit the following links:

More Applications of Matrices and Determinants

Cramers Rule:

www.purplemath.com/modules/cramers.htm

EXTRA! EXTRA! READ ALL ABOUT CRAMER'S RULE ON TEACHER TUBE!

Applications-of-Matrices-and-Determinants