The Gauss-Jordan Elimination Method - Preview

   The elimination method of Gauß and Jordan transforms a given system of linear equations in one which has the same solutions as the original one but which is so simple that one can read off its solutions right away. – For example, Gauß–Jordan elimination transforms the system

of 3 equations with 3 unknowns into the system

of 2 equations with 3 unknowns. The steps taken in this process are designed to ensure that both systems have exactly the same solutions.

   So, what’s the difference between the first system and second system? In the first system it is not easy to see what the solutions are. However, solutions of the second system are easy to read off: For every choice of in ,

1 +     and    2 – 2

is a solution of the system. For example,

   0    yields       1   and      2
   1    yields       2   and      0
   –2    yields       –1   and      6

By design each of these number triples (,,) also solves the first system.