Mathematics for Electrical Engineering and Computing

13.5 Gauss elimination

Gauss elimination is a structured process for the elimination of variables in one of the equations. It is easy to generalize to larger systems of equations and it is relatively numerically stable, making it suitable for use with a computer.

Gauss elimination is performed in stages. At Stage 1, we concentrate on the first column, the coefficients of x. The idea is to make the coefficient of the first equation 1 and eliminate the variable from the other equation(s) by using multiples of the first equation. Equation 1 is therefore the pivotal equation for Stage 1.

Example 13.25

Solve

$\begin{array}{c}3x+4y=7\\ 5x-8y=8\end{array}$

using Gauss elimination.

Solution ...