#uw/notes #uw/class/math208 
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- Not all systems of linear equations will be in echelon form and easily solvable
- There are three **elementary operations** that can be used to create a new system that is equivalent to the old one
	- Interchange the position of two equations
	- Multiply an equation by a nonzero constant
	- Add a multiple of one equation to another
	- $\sim$ is used to indicate the transformation between equivalent linear systems
- matricies can be used to simplify when working with systems of linear equations
	- matricies with all constant terms of a linear system of equations are called a **augmented matrix**
	- $$\begin{align*} a_{11}x_{1} + a_{12}x_{2} + a_{13}  \end{align*}$$