Editing Chinese mathematics (section)

=== Linear algebra ===
[[Writings on reckoning|''The Book of Computations'']] is the first known text to solve systems of equations with two unknowns.{{sfn|Hart|2011|pages=11–85}} There are a total of three sets of problems within ''The Book of Computations'' involving solving systems of equations with the false position method, which again are put into practical terms.{{sfn|Hart|2011|pages=11–85}} Chapter Seven of ''The Nine Chapters on the Mathematical Art'' also deals with solving a system of two equations with two unknowns with the false position method.{{sfn|Hart|2011|pages=11–85}} To solve for the greater of the two unknowns, the false position method instructs the reader to cross-multiply the minor terms or ''zi'' (which are the values given for the excess and deficit) with the major terms ''mu''.{{sfn|Hart|2011|pages=11–85}} To solve for the lesser of the two unknowns, simply add the minor terms together.{{sfn|Hart|2011|pages=11–85}}

Chapter Eight of ''The Nine Chapters on the Mathematical Art'' deals with solving infinite equations with infinite unknowns.{{sfn|Hart|2011|pages=11–85}} This process is referred to as the "fangcheng procedure" throughout the chapter.{{sfn|Hart|2011|pages=11–85}} Many historians chose to leave the term ''fangcheng'' untranslated due to conflicting evidence of what the term means. Many historians translate the word to [[linear algebra]] today. In this chapter, the process of Gaussian elimination and back-substitution are used to solve systems of equations with many unknowns.{{sfn|Hart|2011|pages=11–85}} Problems were done on a counting board and included the use of negative numbers as well as fractions.{{sfn|Hart|2011|pages=11–85}} The counting board was effectively a [[Matrix (mathematics)|matrix]], where the top line is the first variable of one equation and the bottom was the last.{{sfn|Hart|2011|pages=11–85}}