System and matrixes chapter 3
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System and Matrixes Chapter 3. By Kate Hanna, Danielle Pomante , Nasheeba St. Louis. Elimination Eliminate the y. Times Eq. 3 by 2. Eliminate y in Eq. 2&3 Solve new system. Add new equations. Put into original equation & solve for y. 16x+11z=-1 -16x-7z=-11 4z=-12

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System and Matrixes Chapter 3

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System and matrixes chapter 3

System and MatrixesChapter 3

By Kate Hanna, Danielle Pomante, Nasheeba St. Louis


System and matrixes chapter 3

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


Example 1 elimination

Example 1: elimination

Page 182 # 11

3x – y + 2z = 4

6x – 2y + 4z = -8

2x – y + 3z = 10


Substitution

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


Example 2

Example 2:

Page 182 # 17

4x + y + 5z = -40

-3x + 2y + 4z = 10

X – y – 2z = -2


Graphing 3 variable equations

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 3

Example 3:

Page 177 # 6

2x + 9y – 3z = -18 z

y

x


Adding subtracting matrixes

Adding & Subtracting Matrixes


Multiplying matrixes

Multiplying Matrixes


Example 4

Example 4:

Page 196 example 2


Inverse matrixes

Inverse Matrixes

On your calculator:

2nd Matrixes  Edit  1: [A], etc

Enter Numbers 

Inverse A-1 = 2nd, X-1


Practice problems

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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