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1、用消元法解二元線性方程組用消元法解二元線性方程組 .,22221211212111bxaxabxaxa 1 2 :122a ,2212221212211abxaaxaa :212a ,1222221212112abxaaxaa ,得,得兩式相減消去兩式相減消去2x;212221121122211baabxaaaa )(,得,得類似地,消去類似地,消去1x,211211221122211abbaxaaaa )(時(shí)時(shí),當(dāng)當(dāng)021122211 aaaa方程組的解為方程組的解為,211222112122211aaaabaabx )(3.211222112112112aaaaabbax 由方程組的四個(gè)系
2、數(shù)確定由方程組的四個(gè)系數(shù)確定. 由四個(gè)數(shù)排成二行二列(橫排稱行、豎排由四個(gè)數(shù)排成二行二列(橫排稱行、豎排稱列)的數(shù)表稱列)的數(shù)表)4(22211211aaaa)5(42221121121122211aaaaaaaa行行列列式式,并并記記作作)所所確確定定的的二二階階稱稱為為數(shù)數(shù)表表(表表達(dá)達(dá)式式 即即.2112221122211211aaaaaaaaD 11a12a22a12a主對(duì)角線主對(duì)角線副對(duì)角線副對(duì)角線2211aa .2112aa 二階行列式的計(jì)算二階行列式的計(jì)算若記若記,22211211aaaaD .,22221211212111bxaxabxaxa對(duì)于二元線性方程組對(duì)于二元線性方程組
3、系數(shù)行列式系數(shù)行列式 .,22221211212111bxaxabxaxa,22211211aaaaD .,22221211212111bxaxabxaxa,2221211ababD .,22221211212111bxaxabxaxa,22211211aaaaD .,22221211212111bxaxabxaxa,2221211ababD .,22221211212111bxaxabxaxa.2211112babaD 則二元線性方程組的解為則二元線性方程組的解為,2221121122212111aaaaababDDx 注意注意 分母都為原方程組的系數(shù)行列式分母都為原方程組的系數(shù)行列式.2221121122111122aaaababaDDx . 12,12232121xxxx求解二元線性方程組求解二元線性方程組解解1223 D)4(3 , 07 112121 D,14 121232 D,21 DDx11 , 2714 DDx22 . 3721