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Applications-of-Matrices-and-Determinants

last edited by 11 years, 11 months ago

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

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.

More Applications of Matrices and Determinants

people.richland.edu/james/lecture/m116/matrices/applications.html

Cramers Rule:

www.purplemath.com/modules/cramers.htm

www.teachertube.com/view_video.php

Anonymous said

at 12:07 pm on Dec 16, 2008

nice!