#### Introduction

- Given a system of linear equations:
- It can be very time consuming to write this out.
- Instead, we can omit the variables and write the coefficients as a matrix:
- This is called a coefficient matrix
- We can add an extra column to this matrix to also store the values on the right side of the equals sign:
- This is called an augmented matrix.
- Augmented matrices are easier and clearer to work with than fully explicit systems of linear equations.

#### LaTeX

```
\left\[\begin{matrix}
1 & 1 & 1 \\
1 & 2 & 3 \\
3 & 6 & -1
\end{matrix}
\,\,\right|
\left.\begin{matrix}
5 \\
3 \\
1
\end{matrix}\right]
```