4g=(d49 1001 (4)略. 2.计算下列矩阵的运算 /11 /1-11y (四)A=212,B=02-1 231/ 120 /a b c Ic b a 6八 求Aa,A-A-职 /34-2N /608 解（四）AB=441,AB-BA=25-2,(4+BP= 36-1 -23-8/ (2)AB= 人++由8士经+ ac+ba+cb （a-b12 AB-BA- -a-6a-) (a-6)2 (6-c)(a-b) a-9。-2 6-c(a-b) (A+B)2 -(a-b)(a+6-2c)0(a-b)(a+b-2c) -(b-ca+b-2c）0(6-c(a+b-2c) 3.计算 22112 /1-1113 (1)212 (201-1: \122/ \-101 () (6) ·(g ).o /11·…1 /λ10 ()01 (8)(En+A)",A= 00A/ /988 解四898 10A4B4 =   −1 0 0 0 −1 0 0 0 1  . (4) i. 2. xg]^3g: (1) A =   1 1 3 2 1 2 2 3 1  , B =   1 −1 1 0 2 −1 1 2 0  ; (2) A =   a b c b c a c a b  , B =   c b a a c b b a c  ; s AB, AB − BA, (A − B) 2 . : (1) AB =   4 7 0 4 4 1 3 6 −1  , AB − BA =   3 4 −2 2 5 −2 −2 3 −8  , (A + B) 2 =   6 0 8 1 8 4 3 2 6  . (2) AB =   ac + ba + cb ac + ba + cb a2 + b 2 + c 2 ac + ba + cb a2 + b 2 + c 2 ac + ba + cb a 2 + b 2 + c 2 ac + ba + cb ac + ba + cb  , AB − BA =   (b − c)(a − b) −(a − c)(a − b) (a − b) 2 −(a − c)(a − b) (a − b) 2 (b − c)(a − b) (a − b) 2 (b − c)(a − b) −(a − c)(a − b)  , (A + B) 2 =   (a − c)(a + b − 2c) 0 −(a − c)(a + b − 2c) −(a − b)(a + b − 2c) 0 (a − b)(a + b − 2c) −(b − c)(a + b − 2c) 0 (b − c)(a + b − 2c)  . 3. xg: (1)   2 2 1 2 1 2 1 2 2   2 ; (2)   1 −1 1 0 1 −1 −1 0 1   3 ; (3) µ 0 1 1 1 ¶5 ; (4) µ cos θ − sin θ sin θ cos θ ¶n ; (5) ( a b c )   a b c  ; (6)   a b c   ( a b c ); (7)   λ 1 0 0 λ 1 0 0 λ   n ; (8) (λEn + A) n, A =   1 1 · · · 1 1 1 · · · 1 . . . . . . . . . . . . . 1 1 · · · 1   . : (1)   9 8 8 8 9 8 8 8 9  . (2)   −3 −2 5 3 0 −2 −2 3 −3  . (3) µ 3 5 5 8 ¶ . (4) µ cos nθ − sin nθ sin nθ cos nθ ¶ . (5) (a 2 + b 2 + c 2 ). · 10 ·