wisconsin
Chapter 1: Systems of Linear Equations

Chapter 1: Systems of Linear Equations

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Chapter 1: Systems of Linear Equations
1.1 Solutions and Elementary Operations
Example 1.1.1
Example 1.1.2
Elementary Operations
Definition 1.1 Elementary Operations
Theorem 1.1.1
Definition 1.2 Elementary Row Operations
Example 1.1.3
Exercises for 1.1
1.2 Gaussian Elimination
Definition 1.3 Row-Echelon Form (Reduced)
Example 1.2.1
Theorem 1.2.1
Gaussian3Algorithm4
Example 1.2.2
Example 1.2.3
Gaussian Elimination
Example 1.2.4
Rank
Definition 1.4 Rank of a Matrix
Example 1.2.5
Theorem 1.2.2
Example 1.2.6
Exercises for 1.2
1.3 Homogeneous Equations
Example 1.3.1
Theorem 1.3.1
Example 1.3.2
Linear Combinations and Basic Solutions
Example 1.3.3
Example 1.3.4
Example 1.3.5
Definition 1.5 Basic Solutions
Convention:
Theorem 1.3.2
Example 1.3.6
Exercises for 1.3
Exercise 1.3.6
Exercise 1.3.9
1.4 An Application to Network Flow
Junction Rule
Example 1.4.1
Exercises for 1.4
1.5 An Application to Electrical Networks7
Ohm’s Law
Kirchhoff’s Laws
Example 1.5.1
Exercises for 1.5
Exercise 1.5.5
1.6 An Application to Chemical Reactions
Example 1.6.1
Exercises for 1.6
Supplementary Exercises for Chapter 1
Exercise 1.11
Section worksheets