Gauss-Jordan Elimination

In this sequence, the second system is obtained from the first by adding the second equation to the first one. Subtracting the second equation from the new first equation reverts us to the initial system. The same is true for other operations that follow. They are all reversible, which implies that the solution set does not change. The third system arises from the second via a reversible operation, specifically by dividing the first equation by 2. The fourth system is obtained from the third by substraction the first equation from the second. Finally, the last system in the chain derives from its predecessor by multiplying the second equation by −1.