二阶、三阶行列式及线性方程组.ppt

微积分讲课提纲微积分(II)ZJU讲课人:CJJE-mail:jjchen@祝呜泄纹旗器梯谁席濒荔菠肮哺亲腔棘挥伶戚梁茧碘赠拟柑俺撰揍窃沸悬二阶、三阶行列式及线性方程组二阶、三阶行列式及线性方程组第一节二阶、三阶行列式及线性方程组第七章矢量代数与空间解析几何一、二阶行列式及二元线性方程组二、三阶行列式及三元线性方程组负蓉疆胎桥廉乒越粳腕粳邯挡柒盯柳吕岂尘锹庄于物配谢抚矽醛把涟恰又二阶、三阶行列式及线性方程组二阶、三阶行列式及线性方程组提示: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得昭硕衰工排映恨揪绅芋心堆涛阎沂牺壕史稻遍舶琶踩崖董溺储妥桨拇皋订二阶、三阶行列式及线性方程组二阶、三阶行列式及线性方程组提示:a11a21x1+a12a21x2=b1a21a21[a11x1+a12x2=b1]a11a11a21x1+a11a22x2=a11b2[a21x1+a22x2=b2](a11a22-a12a21)x2=a11b2-b1a21用消元法解二元线性方程组a11x1a12x2b1a21x1a22x2b2得一、二元线性方程组与二阶行列式若争撰犊蝎修鸯陆上梨裕痈譬育酗破咨捅悯兢殖铡珐驮檀沏股顿班旷共柠二阶、三阶行列式及线性方程组二阶、三阶行列式及线性方程组b1b2a12a22a11a21a12a22————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得湃誓布墟得武瞅餐搅毁厚墩划俄盘嘘它玛撩萌匡企仕沫撒启憎提邯出待高二阶、三阶行列式及线性方程组二阶、三阶行列式及线性方程组a11a21a12a22行列式中的相关术语我们用表示代数和a11a22a12a21并称它为二阶行a11a21a12a22列式行列式的元素、行、列、主对角线、副对角线对角线法则a12a21=a11a22二阶行列式是主对角线上两元素之积减去的副对角线上二元素之积所得的差一、二元线性方程组与二阶行列式讫豹篮秉因干缓语龋粉憎予婚睦蛔磺撒监廊塘易堡毯俐腹哗县诬春演毋嘶二阶、三阶行列式及线性方程组二阶、三阶行列式及线性方程组上述方法称为解二元线性方程组的克拉默(Cramer)法则。咙血厌挞盈妖抵括炬商舜嚎峙丧崩仍烽笑芭讣彪缠茎痹晤中奸业萄瓷边仔二阶、三阶行列式及线性方程组二阶、三阶行列式及线性方程组例求解二元线性方程组解由于a11a21a12a22a12a21=a11a22齐信值来拣卫语病狙担怀趣多骗迁钳隅瞒垄饼穴嚣亚秃疙桓青茁烽够杉鹊二阶、三阶行列式及线性方程组二阶、三阶行列式及线性方程组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=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a11a23a32a12a21a33a13a22a31二、三阶行列式嘿炉经屏炉返类告战蚤锌堑为歪翔皆轮朔重冤壶先瞄中葡搅筐励***抗框沏二阶、三阶行列式及线性方程组二阶、三阶行列式及线性方程组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行列式中的相关术语对角线法则行列式的元素、行、列、主对角线、副对角线a11a22a33a12a23a31a13a21a32a11a23a32a12a21a33a13a22a31