大学线性代数最全知识点.pptVIP免费

线性代数第一章行列式第二章矩阵及其运算第三章矩阵的初等变换及线性方程组第四章向量组的线性相关性第五章相似矩阵及二次型一、二元线性方程组与二阶行列式用消元法解二元(一次)线性方程组:第一章行列式22221211212111bxaxabxaxa(1)(2)(1)a22:a11a22x1+a12a22x2=b1a22,(2)a12:a12a21x1+a12a22x2=b2a12,两式相减消去x2,得(a11a22–a12a21)x1=b1a22–b2a12;§1.1二阶与三阶行列式;212221121122211baabxaaaa）（，得类似地，消去1x,211211221122211abbaxaaaa）（时，当021122211aaaa方程组的解为，211222112122211aaaabaabx）（3.211222112112112aaaaabbax由方程组的四个系数确定.由四个数排成二行二列（横为行、竖为列）的数表)4(22211211aaaa定义定义)5(42221121121122211aaaaaaaa行列式，并记作）所确定的二阶称为数表（表达式即.2112221122211211aaaaaaaaD11a12a22a12a主对角线副对角线对角线法则对角线法则2211aa.2112aa二阶行列式的计算若记,22211211aaaaD.,22221211212111bxaxabxaxa对于二元线性方程组系数行列式.,22221211212111bxaxabxaxa,22211211aaaaD.,22221211212111bxaxabxaxa,2221211ababD.,22221211212111bxaxabxaxa,22211211aaaaD.,22221211212111bxaxabxaxa,2221211ababD.,22221211212111bxaxabxaxa.2211112babaD则二元线性方程组的解为,2221121122212111aaaaababDDx.2221121122111122aaaababaDDx例例11.12,12232121xxxx求解二元线性方程组解1223D)4(3,07112121D,14121232D,21DDx11,2714DDx22.3721二、三阶行列式定义定义333231232221131211)5(339aaaaaaaaa列的数表行个数排成设有记记,312213332112322311322113312312332211)6(aaaaaaaaaaaaaaaaaa333231232221131211aaaaaaaaa（6）式称为数表（5）所确定的三阶行列式三阶行列式.323122211211aaaaaa.312213332112322311aaaaaaaaa(1)沙路法三阶行列式的计算322113312312332211aaaaaaaaaD333231232221131211aaaaaaaaaD.列标行标333231232221131211aaaaaaaaaD333231232221131211aaaaaaaaa332211aaa.322311aaa(2)(2)对角线法则对角线法则注意红线上三元素的乘积冠以正号，蓝线上三元素的乘积冠以负号．...