1二階三階行列式:22)1(a 1122122222211,a aa abxax:12)2(a 1221122212221,a aa abxax2x兩兩式式相相減減消消去去，得得112212212211221()xa aa aaabb ， )1()2(1x類類似似地地，消消去去，得得112212221111212(),xbba aa aaa 1112112xxaab2122122xxaab 112212212211221()xa aa aaabb ，112212221111212(),xbba aa aaa 時(shí)時(shí)，所所以以當(dāng)當(dāng)021122211 aaaa 221211221211122aaaaxbaba ，112111221212221.aaabbaxaa 2二階三階行列式 1112112xxaab2122122xxaab 221211221211122aaaaxbaba ，112111221212221.aaabbaxaa 11221221a aa aj ia11a12a21a22a( ) ( ) 3二階三階行列式 1112112xxaab2122122xxaab 221211221211122aaaaxbaba ，112111221212221.aaabbaxaa 112222b aa b 1,D 2b1b12a22a111221ab ab 2b1b11a21a2,D D 11a21a12a22a11,xDD 22.xDD 12jDDjbb是是用用常常數(shù)數(shù)項(xiàng)項(xiàng)代代替替的的第第 列列得得, ,到到的的行行列列式式(1,2).j 4二階三階行列式12123212,21.xxxx 求求解解二二元元線線性性方方程程組組1223 D)4(3 7 ,0 1D ,14 DDx11 DDx22 12121 2D 21, 12132147 2, 217 3. 5二階三階行列式933設(shè)設(shè)有有 個(gè)個(gè)數(shù)數(shù)排排成成 行行 列列的的數(shù)數(shù)表表111213212223313233aaaaaaaaa111213212223313233aaaaaaaaa112233122331132132a a aa a aa a a112332122133132231.a a aa a aa a a6二階三階行列式333231232221131211aaaaaaaaa332211aaa 112332.a a a 132132a a a 122331a a a 132231a a a 122133a a a 7二階三階行列式計(jì)計(jì)算算三三階階行行列列式式由對(duì)角線法則由對(duì)角線法則 D1 2 ( 2) 2 1 ( 3) ( 2) 4 ( 4) 1 1 4 2 ( 2) ( 2) ( 4) 2 ( 3) 24843264 .14 124221 .342D 8二階三階行列式121213 .111D 計(jì)計(jì)算算三三階階行行列列式式11( 1)( 2)( 3)( 1)121D 1 1 ( 1)( 2) 2 ( 1)1 1 ( 3) 162143 5. 9二階三階行列式求求解解方方程程2111230.49xx 由對(duì)角線法則，由對(duì)角線法則， 方程左端方程左端D , 652 xx解得解得由由 065 2 xx3.2 xx或或23x4x 18 12 9x 22x 10二階三階行列式 111213212221231231233132331323 bbxxxxxxxxaaaaxaaaaab 333231232221131211aaaaaaaaaD 1213122233233,aaDaaaa 1113221233133,aaDaaaa 1112321223132,aaDaaaa , 0 11,xDD 22,xDD 33.xDD 123bbb123bbb123bbb11二階三階行列式12二階三階行列式11122122aaaa11221221.a aa a 111213212223313233aaaaaaaaa112233122331132132a a aa a aa a a112332122133132231.a a aa a aa a a13二階三階行列式14二階三階行列式( (1642170816421708) ) 15二階三階行列式