The method of Gaussian elimination appears in Chapter Eight, Rectangular Arrays, of the important Chinese mathematical text Jiuzhang suanshu or The Nine Chapters on the Mathematical Art. Its use is illustrated in eighteen problems, with two to five equations. The first reference to the book by this title is dated to 179 CE, but parts of it were written as early as approximately 150 BCE. It was commented on by Liu Hui in the 3rd century.
However, the method was invented in Europe independently by Carl Friedrich Gauss when developing the method of least squares in his 1809 publication Theory of Motion of Heavenly Bodies.
[obtained from Wikipedia: http://en.wikipedia.org/wiki/Gaussian_elimination]
