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Mathematics-Online course: Preparatory Course Mathematics - Linear Algebra and Geometry - Systems of Linear Equations | ||

## Gauss Elimination for an invertible Matrix |

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By Gaussian elimination any LSE with invertible coefficient matrix can be brought to upper triangular form in at most steps. For this purpose all coefficients below the diagonal are successively nullified, that is, after steps the LSE has the form

- If the -th diagonal element (the so called pivot element) equals zero, then the -th equation is interchanged with one of the following equations so that .
- For an appropriate multiple of the
-th equation is subtracted from
the -th equation so that
equals zero:

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automatically generated 1/9/2017 |