The Gaussian Elimination method reduces a system of linear equations to a simpler form. The method works in two stages:
- Forward stage
- Backward (or Back Substitution) stage
Consider the following system of four equations;
a11x1 + a12x2 + a13x3 + a14x4 = b1
a21x1 + a22x2 + a23x3 + a24x4 = b2
a31x1 + a32x2 + a33x3 + a33x3 = b3
a31x1 + a32x2 + a33x3 + a44x4 = b4
Numerous methods have been devised to solve the systems of linear equations. This shows that no single method is best suited to all situations. These methods should be judged on the basis of their speed and accuracy. Speed is of importance in solving large systems because of the large volume of computations involved and accuracy is necessary because of the round-off errors involved in performing these computations.
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