行列式的计算1(二阶行列式)

行列式二阶行列式的运算.,222111cybxacybxa，12211221bababcbcx，12211221babacacay用加减消元法解方程组得)0(1221baba，DDxx，DDyy.,222111cybxacybxa,2211babaD,2211bcbcDx,2211cacaDy,2211babaD，DDxx.,222111cybxacybxa21baD,2211bcbcDx1221bcbcDx，12211221bababcbcx,2211babaD12ba二阶系数行列式的运算定义,2211babaD，DDyy.,222111cybxacybxa1221babaD,2211cacaDy1221cacaDy，12211221babacacay,2211babaD方程组有唯一解0D,0时D,0.2yxDD当.,222111cybxacybxa,2211babaD,2211bcbcDx,2211cacaDy)0(1221baba1221bcbcDx01221cacaDy.方程组有无穷多解212121ccbbaa2121bbaa.,,.1方程组无解至少有一个不为零当yxDD用消元法解二元线性方程组.,22221211212111bxaxabxaxa12:122a,2212221212211abxaaxaa:212a,1222221212112abxaaxaa，得两式相减消去2x;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.)4(22211211aaaa定义)5(42221121121122211aaaaaaaa行列式，并记作）所确定的二阶称为数表（表达式即.2112221122211211aaaaaaaa由四个数排成二行二列（横排称行、竖排称列）的数表11a12a22a21a主对角线副对角线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,2221211ababD，211222112122211aaaabaabx，DDx112122211baabD21122211aaaaDRETURN.,22221211212111bxaxabxaxa,22211211aaaaD.2211112babaD.211222112112112aaaaabbax21122211aaaaD，DDx222112112abbaD则二元线性方程组的解为,2221121122212111aaaaababDDx注意分母都为原方程组的系数行列式..2221121122111122aaaababaDDx.,22221211212111bxaxabxaxa方程组有唯一解0D.,,.1,021方程组无解至少有一个不为零当时DDD.,0.221方程组有无穷多解当DD例1.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