System of Linear Equations
Linear Equation
If we have an equation: 
, we can write this in matrix form:
, we can write this in matrix form:
This is a linear equation, where we have a sequence of variables multiplied by coefficients, more generally, this is a linear equation with n unknown variables, and 
known coefficients, note the a at the beginning:
known coefficients, note the a at the beginning:
In 2 dimension (with two unknowns), this is a line; in 3 dimension, this is a surface.
System of Linear Equations
We have a system of linear equations, 3 equations and 3 unknowns:
We can define these:
Augmented Form
We can write W and v together like this, this is the augmented matrix of the system of linear equations:
- Augmented Matrix:
