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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 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

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

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

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

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

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??

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

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

Objective Review?

- If youd like to review the objectives, click the

button below.

Good luck on the quiz!

- http//TeacherWeb.com/MN/UniversityofMinnesota-Dul

uth/Kimber1160/