线性代数二阶与三阶行列式.ppt

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1、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a11x1a12x2b1a21x1a22x2b2得b1b2a

2、12a22a11a21a12a22————x1a11a21b1b2a11a21a12a22————x2a11a21a12a22我们用符号表示代数和a11a22a12a21这样就有一、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a11x1a12x2b1a21x1a22x2b2得为了便于记忆和计算我们用符号表示代数和a11a21a31a12a22a32a13a23a33D=a11a22a33a12a23a31a13a21a32a11a23a32a12a21a33a13a22a31其中D1=

3、b1a22a33a12a23b3a13b2a32b1a23a32a12b2a33a13a22b3D2=a11b2a33b1a23a31a13a21b3a11a23b3b1a21a33a13b2a31D3=a11a22b3a12b2a31b1a21a32a11b2a32a12a21b3b1a22a31方程组a11x1a12x2a13x3b1a21x1a22x2a23x3b2a31x1a32x2a33x3b3的解为a11a22a33a12a23a31a13a21a32a1

4、1a23a32a12a21a33a13a22a31二、三阶行列式我们用符号表示代数和a11a21a31a12a22a32a13a23a33a11a22a33a12a23a31a13a21a32a11a23a32a12a21a33a13a22a31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a11a22a33a12a23a31a13a21a32a11a23a32a12a21a33a13a22a31二、三阶行列式(2)当0且3时D0(1)当

5、0或3时D0令230则03问当为何值时(1)D0(2)D0例1设D231解D2312310625(1)34015024630(1)104858141200356例2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