二阶和三阶行列式ppt课件

1、 .,22221211212111bxaxabxaxa 1 2 :122a ,2212221212211abxaaxaa :212a ,1222221212112abxaaxaa ，2x;212221121122211baabxaaaa ）（,211211221122211abbaxaaaa ）（，211222112122211aaaabaabx ）（3.211222112112112aaaaabbax ，1x021122211 aaaa22211211aaaa21122211aaaa ）（ 4）（422211211aaaa）（ 5.2112221122211211a aa aa aa aa

2、aa aa aa aD D 11a12a22a21a2211aa ,22211211aaaaD .,22221211212111bxaxabxaxa2112aa .,22221211212111bxaxabxaxa22211211aaaaD .,22221211212111bxaxabxaxa,2221211ababD .,22221211212111bxaxabxaxa,22211211aaaaD .,22221211212111bxaxabxaxa,2221211ababD .,22221211212111bxaxabxaxa.2211112babaD ,2221121122212111a

3、aaaababDDx .2221121122111122aaaababaDDx .12,12232121xxxx1223 D)4(3 , 07 112121 D,14 121232 D,21 DDx11 , 2714 DDx22 . 3721 333231232221131211) 6 (aaaaaaaaa,312213332112322311322113312312332211aaaaaaaaaaaaaaaaaa 333231232221131211aaaaaaaaa）（ 7333231232221131211aaaaaaaaaD 323122211211aaaaaa .3122133321

4、12322311aaaaaaaaa (1)沙路法沙路法三阶行列式的计算三阶行列式的计算322113312312332211aaaaaaaaa D333231232221131211aaaaaaaaaD . .列标列标行标行标333231232221131211aaaaaaaaa332211aaa .322311aaa 322113aaa 312312aaa 312213aaa 332112aaa ;,333323213123232221211313212111bxaxaxabxaxaxabxaxaxa333231232221131211aaaaaaaaaD , 0 ;,333323213123

5、232221211313212111bxaxaxabxaxaxabxaxaxa,3332323222131211aabaabaabD 333231232221131211aaaaaaaaaD 121bbb ;,333323213123232221211313212111bxaxaxabxaxaxabxaxaxa,3332323222131211aabaabaabD ,3332323222131211aabaabaabD ;,333323213123232221211313212111bxaxaxabxaxaxabxaxaxa333231232221131211aaaaaaaaaD ;,3333

6、23213123232221211313212111bxaxaxabxaxaxabxaxaxa,3333123221131112abaabaabaD ;,333323213123232221211313212111bxaxaxabxaxaxabxaxaxa333231232221131211aaaaaaaaaD ;,333323213123232221211313212111bxaxaxabxaxaxabxaxaxa,3333123221131112abaabaabaD ;,333323213123232221211313212111bxaxaxabxaxaxabxaxaxa.33231222

7、21112113baabaabaaD ,3333123221131112abaabaabaD .3323122221112113baabaabaaD ,11DDx ,22DDx .33DDx 333231232221131211aaaaaaaaaD ,3332323222131211aabaabaabD 2-43-122-4-21D D4)2()4()3(12)2(21 )3(2)4()2()2(2411 24843264 .14 .094321112 xx1229184322 xxxxD, 652 xx0652 xx2x3x . 0, 132, 22321321321xxxxxxxxx111

8、312121 D 111 132 121 111 122 131 5 , 0 1103111221 D, 5 1013121212 D,10 0111122213 D, 5 , 111 DDx, 222 DDx. 133 DDx课堂练习1 2 31233种放法种放法123112 32种放法种放法1种放法种放法6123 nnnnP1233 P. 6 nPn )1( n)2( n123 !.n 我们规定各元素之间有一个标准次序我们规定各元素之间有一个标准次序, n 个不同的自然数，规定由小到大为标准个不同的自然数，规定由小到大为标准次序次序. 在一个排列在一个排列 中，若数中，若数 则称这两个数组

9、成一个逆序则称这两个数组成一个逆序. nstiiiii21stii 3 2 5 1 43 2 5 1 413103 2 5 1 40 1 0 3 113010 t. 5 计算下列排列的逆序数，并讨论它们计算下列排列的逆序数，并讨论它们的奇偶性的奇偶性. . 2179863541453689712544310010 t18 54 0100134 321212 nnn12 ,21 nn14 ,4 kkn34 , 24 kkn 1 nt 2 n 32121 nnn1 n 2 n kkkkkk132322212123 0 t kkk 21112,2k kk1 1 2 kkk 112 kkkkk0 1 1 2 2 k，（7)25346110)256431（ 奇排奇排列列 偶排偶排列列2 2 排列具有奇偶性排列具有奇偶性. .3 计算排列逆序数常用的方法有计算排列逆序数常用的方法有2 种种.1 1 个不同的元素的所有排列种数为个不同的元素的所有排列种数为n!.n分别用两种方法求排列分别用两种方法求排列163524