# Coefficient and augmented matrices

## Prerequisites

### Coefficient and augmented matrices

#### 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]