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第一章 行列式,本章主要介绍: 一、行列式的定义与性质 二、克莱姆(Cramer)法则,第一节 二阶与三阶行列式,二、三元线性方程组与三阶行列式,一、二元线性方程组与二阶行列式,提示:,a11a22x1+a12a22x2=b1a22 ,a22,a11x1+a12x2=b1,a12,a12a21x1+a12a22x2=a12b2 ,a21x1+a22x2=b2,(a11a22-a12a21) x1= b1a22 - a12b2 ,一、二元线性方程组与二阶行列式,用消元法解二元线性方程组,a11x1a12x2b1,a21x1a22x2b2,得,这样就有,一、二元线性方程组与二阶行列式,a11a22a33a12a23a31a13a21a32a11a23a32a12a21a33a13a22a31,二、三阶行列式,a11a22a33a12a23a31a13a21a32a11a23a32a12a21a33a13a22a31,并称它为三阶行列式,对角线法则(或用沙路法则),行列式的元素、行、列、主对角线、副对角线,a11a22a33a12a23a31a13a21a32,a11a23a32a12a21a33a13a22a31,二、三阶行列式,(2)当0 且 3时 D0,(1)当0 或 3时 D0,令230,则0 3,解,2,3,106,25(1),340,150,246,30(1),1048,58,小 结,二、三阶行列式 二、三元线性方程组的克莱姆法则,以此介绍 n 阶行列式的定义,
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