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Linear Equations and Matrices

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Linear Equations and Matrices by Meghan Kimber Target Audience This lesson is intended for college freshmen in Finite Mathematics 1160 Objectives To create ... – PowerPoint PPT presentation

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Title: Linear Equations and Matrices


1
Linear Equations and Matrices
  • by Meghan Kimber

2
Target Audience
  • This lesson is intended for college freshmen in
    Finite Mathematics 1160

3
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

4
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
5
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
6
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
7
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
8
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??

9
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
10
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

11
Objective Review?
  • If youd like to review the objectives, click the
    button below.

12
Good luck on the quiz!
  • http//TeacherWeb.com/MN/UniversityofMinnesota-Dul
    uth/Kimber1160/
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