# Chapter 8 - Section 8.1 - Matrix Solutions to Linear Systems - Exercise Set - Page 895: 52

An augmented matrix is the collection of the coefficients of equations of the system.

#### Work Step by Step

A system of linear equations can be solved with the help of matrices. It is solved with the help of an augmented matrix. An augmented matrix is divided into two groups by a vertical bar with the coefficients of the variable on one side and constants on the other side. The coefficient of the missing variable is used as $0$. Example: Consider the system of linear equations, \left\{ \begin{align} & 3a+b-4c=1 \\ & 2a-b+2c=-8 \\ & a+2b-3c=9 \end{align} \right. The augmented matrix for the given system of linear equations can be written as, $\left[ \begin{matrix} 3 & -1 & -4 & 3 \\ 2 & -1 & 2 & -8 \\ 1 & 2 & -3 & 9 \\ \end{matrix} \right]$

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