《九章算术》是我国古代著名的数学专著,其“方程”章中给出了“遍乘直除”的算法解方程组.比如对于方程组,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%7B%3C%2Fmo%3E%3Cmrow%3E%3Cmtable+columnalign%3D%22left%22%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ez%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3Cmtext%3E%E2%91%A0%3C%2Fmtext%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ez%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmtext%3E%E2%91%A1%3C%2Fmtext%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3Ez%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmtext%3E%E2%91%A2%3C%2Fmtext%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 先将方程①中的未知数系数排成数列
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3C%2Fmath%3E)
, 然后执行如下步骤:(如图)第一步,将方程②中的未知数系数乘以3,然后不断地减一行,直到第二行第一个数变为0;第二步,对第三行做同样的操作,其余步骤都类似.
方程①:![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3C%2Fmath%3E)
第一步方程②:![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmtext%3E%E2%8B%AF%3C%2Fmtext%3E%3Cmtext%3E%E2%8B%AF%3C%2Fmtext%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmath%3E)
第二步方程③:![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3Cmi%3EM%3C%2Fmi%3E%3Cmtext%3E%E2%8B%AF%3C%2Fmtext%3E%3Cmtext%3E%E2%8B%AF%3C%2Fmtext%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmn%3E8%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3C%2Fmath%3E)
其实以上步骤的本质就是在消元,根据以上操作,有下列结论:(1)数列M为:
(2)
(3)
其中正确的有( )
- A、(1)(2)
- B、(2)(3)
- C、(1)(3)
- D、(1)(2)(3)