Gaussian algorithm

20-10-2021 à 15:08:17
Gaussian algorithm

One method for solving systems - algebra homework help - of linear equations with three or more unknowns is the Gaussian algorithm (the Gaussian elimination method).

In addition to Cramer's rule - pay someone to do my assignment , the Gaussian algorithm (also called the Gaussian eliminationmethod) can be used to solve linear systems of equations from n equations with n unknowns . 

The Gaussian algorithm makes use of the following transformations:
 - Multiplying an equation by a number (other than zero);
 - Adding two equations

These deformations are equivalent deformations , i.e. that is, they do not change the set of solutions - excel homework help in the system of equations. 

The Gaussian algorithm then consists of the following steps:

1. Rearrange the equation system if necessary (swap equations);

2. Accept the first equation (I) unchanged;

3. Using equation (I), eliminate the first variable (x) of the second and each subsequent equation, for which purpose the above-mentioned transformations are used. Equation (II) becomes equation (II '), (III) becomes (III'), etc.

4. Adopt the first equation (I) and the first transformed equation (II ');
 
5. Using equation (II '), eliminate the second variable (y) in the third and every subsequent equation, for which purpose the above-mentioned transformations are used. Equation (III ') becomes equation (III "), (IV') becomes (IV"), etc.

6. Continue the process (repeat steps 4 and 5 analogously with the next equations) until an equation with an unknown is reached. Together with the equations adopted in the last step, this forms the so-called triangular shape, from which all variables can then be calculated
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