第1章行列式1.4行列式的展開ppt課件

1、23M jiA11121314212224313233344142324344aaaaaaaDaaaaaaaaa 23A 23M ( 1)ij 414244aaa313234aaai ja1n i jMi jajiM2 3( 1) 23M111214aaa23ai ja12M 11131421222324313233344144224143aaaaaaaDaaaaaaaaa 12A 12M ij jiA iiA 233343aaa243444aaa122232aaa132333aaa213141aaa44M 112131aaa1 2( 1) 12M44A 4 4( 1) 44M44M ( 1)

2、ji jiMjiM iiMD j ia ijaijaj iaj iA( 1)ji j iM11121314212223244142334443000aaaaaaaaaaaaa33a 33a 3 3( 1) 122242aaa142444aaa112141aaa33A11a232322223333.nnnnnnaaaaaaaaa1211212220.0.nnnnnaaaaaaa11a 51000372 4 21 231 325145020002 2 5( 1) 531 202 3104 1 4023 52 5 52 314 1 423 510 2 3 12() 07 206 610 ( 2) 7

3、 26 620 ( 42 12) 1080 例例235 211105 1 31324 1 3 ( 2) 511 05 1105 1 31311 00 511 5 115 11 0 5116 205 5 0 3 1( 1) (3010) 40 nD 即即(),ij ija .ij 計(jì)算計(jì)算11a 0,12a 1,13a 2,1.,na 1n 21a 1,22a 0,解解nD 0123 2n 1n 10123n 2n 21014n 3n 3210 5n 4n 2n 3n 4n 5n 011n 2n 3n 4n 011,1na 2n ( 1) 111111 ( 1) 11111 1 ( 1) 111

4、1 1 1 ( 1) 111 1 1 1 ( 1) 11 1 1 1 1 01232n 1n 第1列加到其他每一列111110222201222002 3000222n 000021n 00000(1)n (1)n 1nA1( 1)n 22n nD 其中其中2828頁頁7 73 3）ija ()ija i2ij ij 計(jì)算計(jì)算解解nD 122 222222 22222 3 22222 2 422 22 221n 222 222n第第2 2行行乘乘以以( ( - -1 1) )加加到到其其他他每每一一行行( 1) 222 2221 00 00000 1 00000 0 200 00 0 03n

5、000 0 002n 2 ( 1) 11A(2)!n 11x21x31x11nx 12x22x32x12nx 13x23x33x13nx 11nx 21nx 31nx 11nnx 1nx2nx3nx1nnx ()jixx 12()xx 32()xx 1.()nnxx 31()xx 1()nxx 12.()nxx 2()nxx 11.()nxx i j1 n 41()xx 42()xx 43()xx 13.()nxx 3()nxx 1a2a3a1b2b3b1c2c3c1d2d3d a02b(b)a 2c(c)a 2d(d)a a0b(b)a c(c)a d(d)a a0ba c a d a 11

6、11 (b)a (c)a (d)a 1b2b1c2c1d2d0c(c)b d(d)b 0cb db 1111 (b)a (c)a (d)a (c)b (d)b (d) c a1 b2 c2 dx a a a ( )f x 111112481248 231xxx( )0f x 1(2) (12) (1)x (22) (2)x (2)x 1,x 2,x 2x 1111 ()()()ba ca da12a()ba 321bbab ()()()ba ca da221bccbc aba 22()dbd ad cbc ac ()()()()()b a c a d a c b d b 0002a a a (

7、)()dc a b c d 0()cb ()ca ()da b32bab 1c32cac 1d32dad 0cb 3232cacbab 1a2a4a1b2b4b1c2c4c1d2d4d242ba b 242ca c 242da d 2bab 2cac 2dad ba ca da ()db 221bddbd aba db 3232dadbab 21111.naaa22122.naaa12.nnnnaaa.11121naaa 11211.nAAA 22122naaa 21222.nAAA 12iiinaaa 12.niiiAAA 12111naaa 11211.nAAA 12jjnjaaa 12.

8、jjjnAAA 1100a 12222.naaa122.nnnaaa2100a 100na 110.0a210.0a100.na12222.naaa12222.naaa12222.naaa122.nnnaaa122.nnnaaa122.nnnaaa11A11a 21A12a 1nA1na 111211122.inninnnniaaaaaaaaa11,ijaa 0 12jjnjaaa1ia1jAij ij 0 0 22ijaa 2iania2jA.njA 1ja2janja.1jA2jAnjA 1ia1ia2ia2ia,.,jinnaa niania1ia1 jA2iaina2 jA.jnA 1

9、2344123234134123412 44344124AAAA 31423112342341241234 44344124AAAA 41A0 41A1()ija422A 433A 444A _ 42A43A44A2 3 4 121212120.00.0.00.0.00.0.00000.00.0000.0nnnnddbbaabcccda22221.00. . . . .0.00.0. . . . . . .00000.00.0nnnnadcdbcadb1 21( 1)nb 21222.00.0.00.0.0.00.00000nnnncccdbdaba2nD 1b 12()nD 11a d 1c

10、1211)1(1()nb ca dD 1111()dbac 12211122()()ddbacab c 11212212()().aabbdcdc 12()nD 2222)2(2()nb ca dD 3233)3(3()nb ca dD 2nD 1a 21 1( 1)n ()nnnndab c 2( )1D1111()nnnncabd 5D 5D 1000a b 100abab 010aba b 001abab 000abab 1000a100abab 010aba b 001aba b 000abab 0000b100abab 010aba b 001abab 000abab 0100a00

11、10a0001a0000a5a b 4D5ab 43()abD 542abab 3D32()abD 542 33abab ab 2D21()abD 54233245abab ab ab a b 100a 110b 011c 001d101101bacd 1 2( 1) 1100101cd ()a bcdbd (1)cd 1abcdabadcd 0100 110abb 11ac 001d101101abacd ad 1abcdabadcd 111010abaadccd (1)(1)abcd123312231xxxxxxxxx31x 3110,xpxq 131pqxx 232pqxx 333pqxx 1323()()()xxxxpxqxxx 121232()()xxxxxxxx 12312123133232()()xxxx xx xxxxx x xxx 123, 0 xxx 123x x xq 1233()xxpqx 123x x xq32x 33x 1233x x x 1233x x x 33()0pqq 0 333123xx