System of linear equations/Set of variables/Equivalent system/Manipulations/Fact
Let be a field, and let
be an inhomogeneous system of linear equations over .
Then the following manipulations on this system yield an
- Swapping two equations.
- The multiplication of an equation by a scalar .
- The omitting of an equation, if it occurs twice.
- The duplication of an equation (in the sense to write down the equation again).
- The omitting or adding of a zero row (zero equation).
- The replacement of an equation by the equation that arises if we add to another equation of the system.