| 
  • If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.

  • Stop wasting time looking for files and revisions. Connect your Gmail, DriveDropbox, and Slack accounts and in less than 2 minutes, Dokkio will automatically organize all your file attachments. Learn more and claim your free account.

View
 

Applications-of-Matrices-and-Determinants

Page history last edited by Mark 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

                                                                                                  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

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

 

Cramers Rule:

www.purplemath.com/modules/cramers.htm

 

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

www.teachertube.com/view_video.php

 

Comments (1)

Anonymous said

at 12:07 pm on Dec 16, 2008

nice!

You don't have permission to comment on this page.