二階和三階行列式ppt課件

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)沙路法沙路法三階行列式的計(jì)算三階行列式的計(jì)算322113312312332211aaaaaaaaa D333231232221131211aaaaaaaaaD . .列標(biāo)列標(biāo)行標(biāo)行標(biāo)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課堂練習(xí)1 2 31233種放法種放法123112 32種放法種放法1種放法種放法6123 nnnnP1233 P. 6 nPn )1( n)2( n123 !.n 我們規(guī)定各元素之間有一個標(biāo)準(zhǔn)次序我們規(guī)定各元素之間有一個標(biāo)準(zhǔn)次序, n 個不同的自然數(shù)，規(guī)定由小到大為標(biāo)準(zhǔn)個不同的自然數(shù)，規(guī)定由小到大為標(biāo)準(zhǔn)次序次序. 在一個排列在一個排列 中，若數(shù)中，若數(shù) 則稱這兩個數(shù)組

9、成一個逆序則稱這兩個數(shù)組成一個逆序. nstiiiii21stii 3 2 5 1 43 2 5 1 413103 2 5 1 40 1 0 3 113010 t. 5 計(jì)算下列排列的逆序數(shù)，并討論它們計(jì)算下列排列的逆序數(shù)，并討論它們的奇偶性的奇偶性. . 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 計(jì)算排列逆序數(shù)常用的方法有計(jì)算排列逆序數(shù)常用的方法有2 種種.1 1 個不同的元素的所有排列種數(shù)為個不同的元素的所有排列種數(shù)為n!.n分別用兩種方法求排列分別用兩種方法求排列163524