1、 1. (I) 121323 422 xxxxxx -+ , (II) , ; (I) . 112 212 33 , , , xyy xyy xy =+ =- = (1) 222222 1213113332 444444 yyyyyyyyyy =-+=-+-+ 222 1332 (2)4 yyyy =-+ ; (2) 113 22 33 2, , , zyy zy zy =- = = (3) 222 123 4 zzz =-+ . . (3) (1), 1123 2123 33 11 , 22 11 , 22 , xzzz xzzz xz =+ =-+ = (4) (4) 11 1 22 11
2、 1 22 001 =- T , : 11 111 0 22 0-21 22 11 =110-2011 22 11110 001 1 22 - TAT 100 040 001 - = . (II) 13 22 31 , /2, , zt zt zt = = = 1123 2123 31 ()/2, ()/2, , xttt xttt xt =+ =-+ = 222 123 fttt =+- 11 22 33 , , i, t t t w w w = = = 1123 2123 31 (i)/2, (i)/2, , x x x www www w =+ =-+ = 222 123 f www =
3、+. 2. : 1 2 n l l l O 1 2 n i i i l l l O , 12 n iii L 1,2, n L . : , AB , 222 1122 nn fxxx lll =+L A , 12 222 12 n iiin fyyy lll =+L B . : t ti yx = (1,2,) tn = L , f B f A , A B . 3 . A n , : A n X , 0 = XAX ; : . =- AA , 0 ii a = , ijji aa =- , , () ijijijjiij ijij axxaaxx =+ XAX . 0 ijji aa += ,
4、 ()0 ijjiij ij aaxx =+= XAX . . X , 0 = XAX , 2 111122112111 ()() nnn axaaxxaaxx + L 22 222233223 ()0 nnn axaaxxax += L . , 1122 0 nn aaa = L , ijji aa =- , =- AA . 4 A n , n X , 0 = XAX , = A0 . : A , 0 = XAX , 2 1111212131311 222 nn axaxxaxxaxx + L 22 222232322 220 nnnnn axaxxaxxax += LL . XAX , 1
5、122 0 nn aaa = L , 20 ij a = (,1,2,) ijn = L , = A0 . 5 n , n , ? A B , 1 2 0 0 r d d d = TBTCAC . . : i d 0 11 22 11 0 r r r r r - - - M 1 r + . r ,1,2,1,0 nn - L , 123 n + L (1)(2) 2 nn + = . 6 222 112132233 9912481306071 xxxxxxxxx -+-+ : 99624 613030 243071 - =- - A . 990 , 996 0 6130 - - , |0 A
6、, , . 7 222 112132233 10824228 xxxxxxxxx +-+ : 10412 4214 12141 =- - A . |0 A , 1 |(1)0 2 k k k =+ A , , . ; 9 1 2 1 11 nn iii ii xxx - + = + : 1 1 2 1 1 2 1 1 2 1 1 2 = O OOO O A . A k 1 1 2 21 1 1 12 2 1 | 2 121 1 2 12 1 1 2 k k = O O OOOOOO O O A 210000 3 01000 2 1 4 00100 2 3 1 00000 k k k = +1
7、(1)0 2 k k =+ , , 10 t , 222 123121323 42106 xxxtxxxxxx + 15 43 531 t t = A . , A , 22 15 1 10,40,43301050 4 531 t t tttt t =-=-+- , , 2 2 40, 301050. t tt - -+- , t , . 11 : A , A , . () ijnn =a A , m 111 1 () | m mmm kkkk m kkkk aa aa = L MM L A , , XAX () m YAY . 1 0 (,) m kk bb = L Y0 , 01 (,) n
8、 cc = L X0 , 12 , 0, im i bikkk c = = L XAX , 00 0 XAX , ()0 000 0 m = XAXYAY . 0 Y , () m YAY , () |0 m A . 12 A , : t , t + EA . 11121 21222 12 n n nnnn taaa ataa t aata + + += + L L MMM L EA , k 11121 21222 12 () k k k kkkk taaa ataa t aata + + = + L L V MMM L , t , , 10 2), ()0 k t V , t + EA .
9、13 : A , 1 - A . A , XAX . 1 - = XAY , 24 , 1 - A , 11 () - = AA , 111 () - = XAXYAAAYYAY , 1 - YAY , 1 - A . 14 A n , |0 A , : n 0 X , 0 XAX . |0 A , |0 A , () Rn = A ; A , 1 - = XCY , 11222222 1212 () pPPn yyyyyy - + =+- LL XAXYCACY . , = CXY , 11112211 21122222 1122 1,111,221,1 1122 , , , , nn nn
10、 pppnnp pppnnp nnnnnn cxcxcxy cxcxcxy cxcxcxy cxcxcxy cxcxcxy + += += += += += L L M L L M L 12 0 p yyy = L , 12 1 pPn yyy + = L , 1111221 2112222 1122 1,111,221, 1122 0, 0, 0, 1, 1. nn nn pppnn pppnn nnnnn cxcxcx cxcxcx cxcxcx cxcxcx cxcxcx + += += += += += L L M L L M L |0 C , 012 (,) n aaa = L X , () 00 000111() pnp np - =+-=- 64474486447448 LL XAX , X0 , 0 XAX . 15 A , ()() RR = AAA . () ijmn a = A , X () = 0 AAX , X , = 22 1 ()00 m yy =+= L YAX XAAXYY , = 00 YAX , X = 0 AX . , X = 0 AX , A , () = 0 AAX , X = 0 AAX , = 0 AX = 0 AAX , , ()()()() nRnRRR -=-= AAAAAA .
