Finite Mathematics Solution Sheets

Nicole Stripling, Jul 10, 2017

Table of Contents

  1. Unit 1: Systems of Linear Equations and Matricies
    1. 1.1: Linear System Terminology
    2. 1.1: Solving Systems of Equations with Parameters (E1)
    3. 3.1.1: Matrix Terminology
    4. Input-Output Models
    5. Linear Programming

1.

Unit 1: Systems of Linear Equations and Matricies

  • 1. 1.1: Linear System Terminology
  • 2. 1.1: Solving Systems of Equations with Parameters (E1)
  • 3. 3.1.1: Matrix Terminology
  • 4. Input-Output Models
  • 5. Linear Programming

1.1.

1.1: Linear System Terminology

Definition of Linear System
A [u]system of equations[/u] is a set or collection of equations that we will deal with all together at once.[br][br][u]Linear Equations[/u] deal with equations that graph straight lines.[br]
Types of Solutions for Two Equations in Two Unknowns
[u]Type 1:[/u] [b]Unique Solutions[/b] occur when the two graphs are lines intersecting at a single point. This point is the [i]unique solution[/i].[br][br][u]Type 2:[/u] [b]Inconsistent Solutions[/b] occur when the graphs are distinct parallel lines. Since the two lines will never intersect, there is [i]no solution[/i] common to both equations.[br][br][u]Type 3:[/u] [b]Dependent Equations[/b] have[i] infinitely many solutions[/i]. This means that the graphs are the same.
Example of a Type 1 System with a UNIQUE SOLUTION
Example of a Type 2 System with NO SOLUTION
Example of a Type 3 System with INFINITELY MANY SOLUTIONS
– Nicole Stripling

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