第一次作业 1计算下列行列式 183 =2×(-4)×3+1×8×1-1×(-4)×(-1)-(-1)×8×2=-24+8-4+16=-4 54 2)15123|=215123|=103123|=0 20321220321243212 bd - cd de=adf b -c e=abcdef 1 -1 1=abcdef 0 -2 0=4abcdej C 0 2证明下列各式 b2 1)2aa+b2b=(a-b) 111 a2 ab b2a2-b2 b(a-b) 2ab+b200 证明:2aa+b2b=2a-2ba-b0=2a-2ba-b0=(a-b X 2)yx+yx|=-2(x3+y2) ty x 证明: y x+y 2(x+y) y x+ y xty x (x+y)1 x+y x+yx x+I x =2(x+y)0xy=2(x+-x2x-y)=-2(x2+y) x 3求下列各排列的逆序数 )13478269(1347826=0+0+0+0+4+2=6 2)987654321t(987654321)=1+2+3+4+5+6+7+8=36ԛྡྷұᆴྜ 1.䅵ㅫϟ߫㸠߫ᓣ 1) 201 1 41 18 3 - - - = = ´ - ´ + ´ ´ - ´ - ´ - - - ´ ´ =- + - + =- 2 ( 4) 3 1 8 1 1 ( 4) ( 1) ( 1) 8 2 24 8 4 16 4 2) 10 8 2 15 12 3 20 32 12 = 5 4 1 14 1 2 15 12 3 10 3 12 3 0 20 32 12 4 32 12 = = 3) 11 1 11 1 1 11 0 20 4 1 1 1 00 2 ab ac ae b c e bd cd de adf b c e abcdef abcdef abcdef bf cf ef b c e - -- - = - = -= - = -- - - 2.䆕ᯢϟ߫৘ᓣ 1) 2 2 3 2 2( ) 111 a ab b aab b ab + =- 䆕ᯢ˖ 2 2 22 2 2 3 ( )0 2 0 0 2 2 2 2 0 2 2 0( ) 1 1 1 1 1 1 1 11 a ab b a b b a b a ab b aab b a b ab a b ab ab - - -+ + = - - = - - =- 2) 3 3 2( ) x y xy y xy x x y xy x y + + =- + + 䆕ᯢ˖ 2 2 33 2( ) 1 2( ) 2( ) 1 2( ) 1 1 2( ) 0 2( )( ) 2( ) 0 x y xy xy y xy y xy y xy x xy xy x xy xy x xy x y xy x y x y y xy x y x y x y x xy y x y xy x ++ + + + = + + =+ + + + + = + - = + - + - =- + - - 3.∖ϟ߫৘ᥦ߫ⱘ䗚ᑣ᭄ 1) 13478269 t(1347826)=0+0+0+0+4+2=6 2) 987654321 t(987654321)=1+2+3+4+5+6+7+8=36