The Nine Chapters on the Mathematical Art
The method of Gaussian elimination appears - albeit without proof - in the Chinese mathematical text Chapter Eight: "Rectangular Arrays" of "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 AD, but parts of it were written as early as approximately 150 BC. It was commented on by Liu Hui in the 3rd century.