Linear Equations and Matrices

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Linear Equations and Matrices

• by Meghan Kimber

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Target Audience

• This lesson is intended for college freshmen in
  Finite Mathematics 1160

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Objectives

• To create coefficient, constant, and augmented
  matrices from linear equations

• To be able to write linear equations given a
  matrix

• To understand and use double subscript notation

• Identify methods to solve a system of linear
  equations

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From Linear Equations to Coefficient Matrices

• Example 1
• 3x - 2y 10
• -6x 4y -7

• A 3 -2
• -6 4

You Try 1 -2x - 2y 10 7x 5y -3
B -2 -2 7 5
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From Linear Equations to Constant Matrices

• Example 2
• 3x - 2y 10
• -6x 4y -7

• A 10
• -7

You Try 2 -2x - 2y 10 7x 5y -3
B 10 -3
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From Linear Equations to Augmented Matrices
Example 3 3x - 2y 10 -6x 4y -7
A 3 -2 10 -6 4 -7
B -2 -2 10 7 5 -3
You Try 3 -2x - 2y 10 7x 5y -3
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From an Augmented Matrix to Linear Equations
Example 4
A -4 8 53 -1 5 -7
Equations -4x 8y 53 -1x 5y -7
You Try 4
B -22 -4 17 -6 5 9
Equations -22x - 4y 17 -6x 5y 9
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Double Subscript Notation

• Double subscript notation describes the location
  of a number in a matrix

• The first subscript number represents the row and
  the second subscript number represents the column

• Generally Arowcolumn or A??

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Double Subscript Notatioin

• Identify the following values or positions
• A23 8
• A12 -3

7 -2
A32 A13
A 3 -2 -3 -6 4 7 -8 8
1
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Methods to Solve a Linear System or Matrix

• Graphing
• Elimination
• Eliminating a variable algebraically
• Row Operations
• Interchanging rows
• Multiplying a row by a constant
• Multiplying a row by a constant and adding it to
  another row

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Objective Review?

• If youd like to review the objectives, click the
  button below.

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Good luck on the quiz!

• http//TeacherWeb.com/MN/UniversityofMinnesota-Dul
  uth/Kimber1160/