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System and Matrixes Chapter 3PowerPoint Presentation

System and Matrixes Chapter 3

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### System and MatrixesChapter 3

By Kate Hanna, Danielle Pomante, Nasheeba St. Louis

EliminationEliminate the y. Times Eq. 3 by 2.Eliminate y in Eq. 2&3Solve new system. Add new equations.Put into original equation & solve for y.

16x+11z=-1

-16x-7z=-11

4z=-12

z=-3

16x+11(-3)=-2

x=2

6x-y+4z=-1

6(2)-y+4(-3)=-1

y=1

x=2, y=1, z=-3

Ordered triple=(2,1,-3)

4x+2y+3z=1

2x-3y+5z=-14

6x-y+4z=-1

4x+2y+3z=1

+12x-2y+8z=-2

16x+11z=-1

2x-3y+5z=-14

-18x+3y-12z=3

-16x-7z=-11

Substitution

x + y + z = 4

x + y - z = -4

3x + 3y + z = 12

- Make one equation equal to one variable.
x + y + z = 4 x= -y - z + 4

- Then plug x into the equation

Graphing 3 Variable Equations

3x + 4y + 12z

- Find the intercept of each variable
3(0) + 4(0) + 6z = 12

6z=12 z=2 Point: (0, 0, 2)

3(0) + 4y + 6(0) = 12

4y = 12 y=3 Point: (0, 3, 0)

3x + 4(0) + 6(0) = 12

3x = 12 x=4 Point: (4, 0, 0)

- Plot each point on 3-axis graph.

Example 4:

Page 196 example 2

Inverse Matrixes

On your calculator:

2nd Matrixes Edit 1: [A], etc

Enter Numbers

Inverse A-1 = 2nd, X-1

Practice Problems !

Solve 2 Variable Equations – p 156

Graph Systems of Linear Equations – p 171

Solve 3 Variable Equations – p 182-183

Basic Matrixes – p 191

Multiplying Matrixes – p 199-200

Inverse – p 214

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