課題：三階行列式羅田縣理工中等專業(yè)學(xué)校周復(fù)元三階行列式333231232221131211)5(339aaaaaaaaa列的數(shù)表列的數(shù)表行行個(gè)數(shù)排成個(gè)數(shù)排成設(shè)有設(shè)有,312213332112322311322113312312332211)6(aaaaaaaaaaaaaaaaaa 333231232221131211aaaaaaaaa（6 6）式稱為數(shù)表（）式稱為數(shù)表（5 5）所確定的）所確定的.323122211211aaaaaa .312213332112322311aaaaaaaaa (1)(1)沙沙路法路法三階行列式的計(jì)算三階行列式的計(jì)算322113312312332211aaaaaaaaa D333231232221131211aaaaaaaaaD.列標(biāo)列標(biāo)行標(biāo)行標(biāo)333231232221131211aaaaaaaaaD 333231232221131211aaaaaaaaa332211aaa.322311aaa 注意注意 紅線上三元素的乘積冠以正號(hào)，藍(lán)線上三紅線上三元素的乘積冠以正號(hào)，藍(lán)線上三元素的乘積冠以負(fù)號(hào)元素的乘積冠以負(fù)號(hào)說明說明1 對(duì)角線法則只適用于二階與三階行列式對(duì)角線法則只適用于二階與三階行列式322113aaa 312312aaa 312213aaa 332112aaa 如果三元線性方程組如果三元線性方程組 ;,333323213123232221211313212111bxaxaxabxaxaxabxaxaxa的系數(shù)行列式的系數(shù)行列式333231232221131211aaaaaaaaaD ,0 利用三階行列式求解三元線性方程組利用三階行列式求解三元線性方程組 2 2.三階行列式包括三階行列式包括3!3!項(xiàng)項(xiàng),每一項(xiàng)都是位于不同行每一項(xiàng)都是位于不同行,不同列的三個(gè)元素的乘積不同列的三個(gè)元素的乘積,其中三項(xiàng)為正其中三項(xiàng)為正,三項(xiàng)為三項(xiàng)為負(fù)負(fù).;,333323213123232221211313212111bxaxaxabxaxaxabxaxaxa,3332323222131211aabaabaabD 若記若記333231232221131211aaaaaaaaaD 或或 121bbb ;,333323213123232221211313212111bxaxaxabxaxaxabxaxaxa,3332323222131211aabaabaabD 記記,3332323222131211aabaabaabD 即即 ;,333323213123232221211313212111bxaxaxabxaxaxabxaxaxa333231232221131211aaaaaaaaaD ;,333323213123232221211313212111bxaxaxabxaxaxabxaxaxa,3333123221131112abaabaabaD 得得 ;,333323213123232221211313212111bxaxaxabxaxaxabxaxaxa333231232221131211aaaaaaaaaD ;,333323213123232221211313212111bxaxaxabxaxaxabxaxaxa,3333123221131112abaabaabaD 得得 ;,333323213123232221211313212111bxaxaxabxaxaxabxaxaxa.3323122221112113baabaabaaD ,3333123221131112abaabaabaD .3323122221112113baabaabaaD 則三元線性方程組的解為則三元線性方程組的解為:,11DDx ,22DDx .33DDx 333231232221131211aaaaaaaaaD ,3332323222131211aabaabaabD 2-43-122-4-21D 計(jì)算三階行列式計(jì)算三階行列式按對(duì)角線法則，有按對(duì)角線法則，有 D4)2()4()3(12)2(21 )3(2)4()2()2(2411 24843264 .14 .094321112 xx求求解解方方程程方程左端方程左端1229184322 xxxxD,652 xx解得解得由由052 xx3.2 xx或或例例4 4 解線性方程解線性方程組組 .0,132,22321321321xxxxxxxxx由于方程組的系數(shù)行列式由于方程組的系數(shù)行列式111312121 D 111 132 121 111 122 131 5 ,0 同理可同理可得得1103111221 D,5 1013121212 D,10 0111122213 D,5 故方程組的解為故方程組的解為:,111 DDx,222 DDx.133 DDx 二階和三階行列式是由解二元和三元線性二階和三階行列式是由解二元和三元線性方方程組引入的程組引入的.對(duì)角線法則對(duì)角線法則二階與三階行列式的計(jì)算二階與三階行列式的計(jì)算.2112221122211211aaaaaaaa ,312213332112322311322113312312332211aaaaaaaaaaaaaaaaaa 333231232221131211aaaaaaaaa二、小結(jié) 使使求一個(gè)二次多項(xiàng)式求一個(gè)二次多項(xiàng)式,xf .283,32,01 fff解解設(shè)所求的二次多項(xiàng)式為設(shè)所求的二次多項(xiàng)式為 ,2cbxaxxf 由題意得由題意得 ,01 cbaf ,3242 cbaf ,28393 cbaf得一個(gè)關(guān)于未知數(shù)得一個(gè)關(guān)于未知數(shù) 的線性方程組的線性方程組,cba,又又,020 D.20,60,40321 DDD得得,21 DDa,32 DDb13 DDc .1322 xxxf故所求多項(xiàng)式故所求多項(xiàng)式為為