Gauss Elimination Method

The Gauss elimination method is to transform a system of equations into an equivalent system that is in triangular form.

To facilitate the calculation, transform the system into a matrix and place the coefficients of the variables and the independent terms into the matrix (separated by a straight line).

Gauss Elimination Method Gauss Elimination Method


Example:

3x +2y + z = 1 cierre
5x +3y +4z = 2
x + y - z = 1

Change the position of row 3 to where row 1 is and shift the other rows down accordingly:

Gauss Elimination Method

Subtract row 2 by three times the value of row 1 and subtract row 3 by five times the value of row 1.

Subtract row 3 by twice the value of row 2.

Gauss Elimination Method

System of Equations

Gauss Elimination Method

Consistent Independent System

Gauss Elimination Method Solution


System of Equations

Gauss Elimination Method

Gauss Elimination Method

Gauss Elimination Method

Gauss Elimination Method

System of Equations

Consistent Dependent System

Gauss Elimination Method Operations

Gauss Elimination Method Operations

Gauss Elimination Method Solution


System of Equations

Gauss Elimination Method

Gauss Elimination Method

Gauss Elimination Method

Gauss Elimination Method

Inconsistent System

Examples:

1System of Equations

Gauss Elimination Method

Consistent Independent System

Gauss Elimination Method Solution

2System of Equations

Gauss Elimination Method

Consistent Dependent System

Gauss Elimination Method

Gauss Elimination Method

Gauss Elimination Method Solution


3System of Equations

Gauss Elimination Method

Consistent Independent System

Gauss Elimination Method Solution


4System of Equations

Gauss Elimination Method

Gauss Elimination Method

Consistent Dependent System

Gauss Elimination Method Solution

Gauss Elimination Method Solution

Gauss Elimination Method

Gauss Elimination Method Solution


5System of Equations

Gauss Elimination Method

Gauss Elimination Method

Gauss Elimination Method

Gauss Elimination Method

Consistent Independent System

Gauss Elimination Method Solution


6System of Equations

Gauss Elimination Method