Solving linear equations

A system of linear equations

\begin{displaymath}
\begin{array}{rrrr}
x_1 & -2 x_2 & + x_3 = & 0 \\
& 2 x_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.



Subsections

Department of Mathematics
Last modified: 2005-10-21