Linear Algebra Systems of Linear Equations 

HH  
What is a Linear Equation?  
A System of Linear Equations 

this system is inconsistent there is no solution 

this system is consistent the solution is unique (1,3) 
this system is consistent there are infinite solutions 

Grapher  
Our goal is to solve this sytem of equations by utilizing the Matrix of coefficients.  
Row Reduction (Gaussian Elimination) 'getting the Matrix in echelon or reduced echelon form' By applying these 3 Elementary Row Operations to our Matrix we will find a solution, if one exists. 



Chapter 1 Sec 1 Problems 19, 20, 21, 22 

Special Cases  
Which columns are the pivot columns and what is the solution set? Chapter 1 Sec 2 Problems 8, 9 

Vector Equations ( another perspective on systems of equations)  
These vectors are odered pairs of points in 2space (in a plane)  
Grapher Chapter 1 Section 1.3 Problems 17, 18, 25, 26 

The Matrix Equation Ax = b 

The equation Ax = b has a solution if and only if b is a linear combination of the columns of A 

Homogeneous Linear Systems (Ax = 0)  


Suppose Ax = b has a solution, explain why the solution is unique (Geometric argument using Theorem 6.) Since Ax = b is consistent, its solution set is obtained by 

Chapter 1 Section 7 Problem 6, 7  