20130215221328_366619922639.pptVIP免费

一一..克拉默克拉默(Cramer)(Cramer)法则法则G.G.CramerCramer[[瑞士瑞士]]((1704.7.311704.7.31~~1752.1.41752.1.4))C.C.MaclaurinMaclaurin[[英英]]((1698.2.?1698.2.?~~1746.6.141746.6.14))第3节克拉默法则aa1111xx11++aa1212xx22+…++…+aa11nnxxnn==bb11aa2121xx11++aa2222xx22+…+…aa22nnxxnn==bb22……………………………………aann11xx11++aann22xx22+…++…+aannnnxxnn==bbnn当当DD00时有唯一解时有唯一解::((ii=1,…,=1,…,nn),),xxii==DDiiDDaa1111aa1212……aa11nnaa2121aa2222……aa22nn……………………aann11aann22……aannnn,,其中其中DD==bb11aa1212……aa11nnbb22aa2222……aa22nn……………………bbnnaann22……aannnn,,DD11==定理定理66..((克拉默法则克拉默法则))线性方程组线性方程组aa1111aa1212……aa11nnaa2121aa2222……aa22nn……………………aann11aann22……aannnn,,其中其中DD==aa1111bb11……aa11nnaa2121bb22……aa22nn……………………aann11bbnn……aannnn,,DD22==aa1111xx11++aa1212xx22+…++…+aa11nnxxnn==bb11aa2121xx11++aa2222xx22+…+…aa22nnxxnn==bb22……………………………………aann11xx11++aann22xx22+…++…+aannnnxxnn==bbnn当当DD00时有唯一解时有唯一解::((ii=1,…,=1,…,nn),),xxii==DDiiDD定理定理6.6.((克拉默法则克拉默法则))线性方程组线性方程组aa1111aa1212……aa11nnaa2121aa2222……aa22nn……………………aann11aann22……aannnn,,其中其中DD==……aa1111……aa1,1,nn11bb11aa2121……aa2,2,nn11bb22……………………aann11……aann,,nn11bbnn..DDnn==aa1111xx11++aa1212xx22+…++…+aa11nnxxnn==bb11aa2121xx11++aa2222xx22+…+…aa22nnxxnn==bb22……………………………………aann11xx11++aann22xx22+…++…+aannnnxxnn==bbnn当当DD00时有唯一解时有唯一解::((ii=1,…,=1,…,nn),),xxii==DDiiDD定理定理6.6.((克拉默法则克拉默法则))线性方程组线性方程组例1.解线性方程组解:方程组的系数行列式故方程组有唯一解.2151130602121476D121306215102121476rr21412130607513021207712rrrr23313060127021207712rr324227130601270031200737rrrr432130601270031200113rr34130601270011300312rr4331306012727,0011300027rr...