Gauss-Jordan elimination

Dividing equations by coefficients and subtracting equations {Gauss-Jordan elimination} can solve equation systems.

process

Divide first row by first-variable coefficient {pivot element}, so first-variable coefficient is one. For other rows, subtract multiple of first row to make first-variable coefficient equal zero, and replace row with resulting row.

Divide new second row by second-variable coefficient, so second-variable coefficient is one. For other rows, subtract multiple of second row to make second-variable coefficient equal zero, and replace row with resulting row.

Follow same steps for all rows. Use pivoting to avoid dividing by zero.

result

All rows begin with variable with coefficient equal one. All rows begin with different variables: row n begins with nth variable.

Whole Section in One File

3-Algebra-Equation-System-Solution

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Technical Information

Date Modified: 2022.0224