Chapter 8

By Briana, Brandon, Kyle, and Michaela

Vocab

• Matrix• Augmented Matrix• Coefficient Matrix• Scalar Multiplication• Reduced Row Echelon Form• Gauss-Jordan Elimination• Inverse Matrix• Determinant• Cramer's Rule

Concepts/Formulas• Gauss-Jordan Elimination: uses augmented matrices to solve systems of

linear equationsWithout a Calculator:1. Write system as Augmented Matrix2. Using row operations work down, around, and up to obtain RREF(see number 4)With a Calculator:3. Hit 2nd then matrix4. Arrow over to edit and hit enter then put in the dimensions3. Hit 2nd quit and then hit 2nd matrix and arrow over to math4. Go to letter B( which is rref)5. Hit 2nd matrix and click enter on the desired one(see number 6)

Concepts/Formulas cont…

• Inverse Matrices:

• Inverse with Calculator:1. Enter the matrix into the calculator2. hit matrix then A then enter and then x-1

Uses: Used to solve a coefficient matrix equation

(see number 5)

ac

bdbcadA )/(11

Concepts/Formulas cont…

• Determinant:(See number 3)

• With Calculator: 1. Hit 2nd matrix and enter the dimensions2. Hit 2nd matrix and arrow over to math and click 1 and hit

enter.3. Click second and pick the matrix you want.

Cramer’s Rule:(see number 8&9)

bcaddc

baA )det(

DDz

DDy

DDx

z

y

x

/

,/

,/

Concepts/Formulas cont…

• Triangle area:

• Test for Collinear Points: 3 points are collinear if and only if:

1

1

1

)2/1(

33

22

11

yx

yx

yx

a

0

1

1

1

33

22

11

yx

yx

yx

Problem Set• 1. What is the order of this matrix?

• 2.

• 3. Find the value of

• 4. Solve the system using Gauss-Jordan Elimination5x+4y=2-x+y=-22

• 5. Find the Inverse, if it exists, of • 6. Solve using Gauss-Jordan Elimination using calculator

211

27

45

211

27

45

4020

124

42

58

45

56

262

52

422

zyx

yx

zyx

• 7. Write the original augmented matrix to solve the system.

• 8. Solve this system using Cramer's Rule.

• 9. Solve using Cramer's Rule.

• 10. A corporation has 4 factories, each of which manufactures 3 types of cordless power tools. The number of cordless power tools produced at each factory in one day is represented by each entry in this matrix.

• Find the production levels if the production is decreased by 5%

501006090

20803050

40907080

572

84

yx

yx

23311

625

yx

yx

543

12

yx

yx