Matrix Algebra

Augmented Matrix

Augmented Matrix. A system of linear equations

$\begin{displaymath} \begin{array}{rrrr} x_1 & -2 x_2 & + x_3 = & 0 \\ & 2 ... ...8 x_3 = & 8 \\ -4 x_1 & +5 x_2 & +9 x_3 = & -9 \end{array} \end{displaymath}$

can be represented by the augmented matrix

$\displaystyle C = \left[\begin{array}{rrrr} 1 & -2 & 1 & 0 \\ 0 & 2 & -8 & 8 \\ -4 & 5 & 9 & -9 \end{array}\right] .$

This matrix enables us to analyze the system of linear equations, and to find a solution if it exists.