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????A2 Mn(K)? ?? ????(A)?? ????? ??? ?????? ??A? J=0 B @11 ???(1)??? 111
C A? ???????J:A:J=(A):J? M=a b c d 2 M 2(R) ????0dcba??b+ca+d? ???? ????n2? ?? ???? M n=anbn c ndn b n+cnan+dn? A=0 @1 0 1 0 4 2

0 0 161

A

A+A1= In?

????A= (ai;j)2 Mn(K)? ??????? ???

8B2 Mn(K);AB=BA() 92K;A=:In?

M n(K)?

C(A) =M2 Mn(C);AM=MA?

??????? ???(Ak)0kn1??? ??? ???? ??C(A)? ????n2N????n2?

A2 Mn(R)8M2GLn(R);AM=MA=In2R?

8M;N2 Mn(R);A=MN=)A=NM?

??????? ????? ??????2R??? ???A=In ??????D= diag(a1;:::;an)2 Mn(K)?? ':M2 Mn(K)7!DMMD? A=0 @1 1 1 0 1 1

0 0 11

A ?? ?? ????B=AI? A=0 @1 1 0 0 1 1

0 0 11

A A=12 3 4 X

23X+ 2?

A=0 B

BBB@1 1

0 1 00 11 C

CCCA2 M

n(R)? A=a b c d 2 M 2(K)? A

2(a+d)A+ (adbc)I= 0?

???A=0 @1 01 2 13

1 0 21

A???B=0

@1 0 1 21 1
1 111

A???C=0

@1 11 2 0 1 2 111 A A=0 B @1 (1) 0 11 C

A2 Mn(R)

??????n2Nn f0;1g??!= exp2in

A=!(k1)(`1)

1k;`n2 Mn(C)?

A=0 @21 2 53 3
1 021 A ????A= (1i;j)2 Mn(R)

B= (IA)(I+A)1?

??? ??????? B= (I+A)1(IA)?

ABC= On?

A=0 B

B@0 1 1 1

1 0 1 1

1 1 0 1

1 1 1 01

C CA ???A=0 B

BBB@1a(0)

???a (0) 11 C CCCA ???B=0 B @1 (1) (0) 11 C

A???C=0

B

BBB@1 2n

???2 (0) 11 C CCCA M n(R)?

M(a;b;c) =0

@a b c 0a b 0 0a1 A ????a;b;c2R?

P() = (i;(j))1i;jn2 Mn(R)

8(;0)2 S2n;P(0) =P()P(0)?

tP()=P(1)?

A=a+b b

b ab ????(a;b)2K2?

8(i;j)2J1;nK2;an+1i;n+1j=ai;j?

f:R3!R2 (x;y;z)7!(x+y;y2x+z) f:R3!R3 (x;y;z)7!(y+z;z+x;x+y)???f:R3[X]!R3[X]

P7!P(X+ 1)

f:R3[X]!R4

P7!P(1);P(2);P(3);P(4)

P=(x;y;z)2R3x+ 2yz= 0??D= Vect(w)??w= (1;0;1)?

? ??????? ??????? ?? p????B? a i;j=j1 i1 ??????a2C??f:C!C?????? ???f(z) =z+az? (1;i)? 0 @0 0 0 1 0 0

0 1 01

A f n= 0??fn16= 0?

B=x;f(x);f2(x);:::;fn1(x)????? ??? ???? ??E?

g2 L(E)gf=fg= Vect(Id;f;f2;:::;fn1)? A=0 @211 1 01 11 01 A A=0 @211 1 21 11 21 A f???? ????? ????? ??fn16= 0? Mat

B(f) =0

B

BBB@0 1 0

???1 0 01 C CCCA? ?????y=x+f2(x)??z=f2(x)?

E= KerfKer(f2+ Id)?

????? ??dimKer(f2+ Id)1? ??????? ???? ??x2Ker(f2+ Id)n f0g????? (x;f(x))??? ??? ??????? ????? ??Ker(f2+ Id)??????? ? ???det(Id)? ?? ???????dimKer(f2+ Id) = 2? 0 @0 0 0 0 01

0 1 01

A A=0 @3 13 1 1 1 1 111 A ?? ????"1= (1;1;1);"2= (1;1;0);"3= (1;0;1)??B0= ("1;"2;"3)? ?????? ?? ??????? ?? f???? ????? ????? 0 @2 11 0 1 0

1 1 01

A ???? C= ("1;"2;"3)????"1= (1;0;1);"2= (1;1;0);"3= (1;1;1)? ??????? ???C??? ??? ????? A=0 @21 0 2 12

1 1 31

A 8<

1=e1+e2e3

2=e1e3

3=e1e2?

??? ??????? B0??? ??? ???? ??E?? ?????? ?? ???????D??f????B0? A=0 @422 1 01 3211
A ??D=0 @0 0 0 0 1 0

0 0 21

A ????C????D? ?? ??????? ? ?????? ??????? ??? ?????? (xn)n2N;(yn)n2N??(zn)n2N??????? ??? ?8< :x 0= 1 y 0= 0 z

0= 0??8n2N;8

:x n+1= 4xn2(yn+zn) y n+1=xnzn z n+1= 3xn2ynzn? ??P?? ??????? ?? ??????? ??b?B? ????x2E? ?????? v= Matbx??V= MatBx? ????? ?f2 L(E)?? m= Matbf??M= MatBf? ????f2 L(E)???? ?? ??????? ???? ?? ????e??? A=0 @0 1 1 0 1 0

1 1 21

A ?? ????e01=e1+e3?e02=e1+e2??e03=e1+e2+e3? ???????B??f????e0? ????f2 L(E)???? ?? ??????? ???? ?? ????B??? A=0 @0 2 1 1 2 1

0 1 11

A ?? ????"1=e1+e3?"2=e1+e2??"3=e1+e2+e3? f????B0? A=0 @32 2 1 2 0

1 1 11

A

1;2??3?

???(x1;x2;x3)????x1= (1;1;0);x2= (1;0;1)??x3= (0;1;1) ???(x1;x2;x3)????x1= (2;1;1);x2= (1;2;1)??x3= (1;1;2) ???(x1;x2;x3)????x1= (1;2;1);x2= (1;0;3)??x3= (1;1;2)? ???f:K3!K3?????? ??? f(x;y;z) = (x+y+z;xy+z;x+yz)? ???f:K3!K3?????? ??? f(x;y;z) = (xy;yz;zx)? ???f:K4!K4?????? ??? f(x;y;z;t) = (x+yt;x+z+ 2t;2x+yz+t;x+ 2y+z)? 0 @1 1 1 b+c c+a a+b bc ca ab1 A 0 @1 coscos2 coscos2cos3 cos2cos3cos41 A???0 B

BBB@a b(0)

(0) ???b b(0)a1 C CCCA ??????n2N??M2 Mn(R)?????? ??? M=0 B

BBBBBB@1 1 00

0 1 1 0 ??????1

1 00 11

C ??????A2 M3;2(R)??B2 M2;3(R)?????? ??? AB=0 @1 0 0 0 1 0

0 0 01

A ???????BA=I2? ???F=(x;y;z)2R3x+my+z= 0 mx+y+mz= 0 ???F=(x;y;z)2R38< :x+y+mz= 0 x+my+z= 0 mx+y+z= 0

F=(x;y;z)2R3x+my+z= 0??mx+ymz= 0

G=(x;y;z)2R3xmy+z= 0?

???8 :xy+z=m x+myz= 1 xyz= 1 ???8 :mx+y+z= 1 x+my+z=m x+y+mz=m2 8 :mx+y+z+t= 1 x+my+z+t=m x+y+mz+t=m+ 1 8< :ax+by+z= 1 x+aby+z=b x+by+az= 1?

8>>>>><

>>>>:x

1+x2+x3++xn= 1

x

1+ 2x2+ 2x3++ 2xn= 1

x

1+ 2x2+ 3x3++ 3xn= 1

x

8>>>>>>><

>>>>>>:x

1+x2= 0

x

1+x2+x3= 0

x

2+x3+x4= 0

x n2+xn1+xn= 0 x n1+xn= 0? z

1;:::;zn??? ??? ?

a i??? ?? ?????? ??[zi;zi+1]??an??? ?? ?????? ??[zn;z1]? 8< :ax+ 2by+ 2z= 1

2x+aby+ 2z=b

2x+ 2by+az= 1?

8>>< >:ax+y+z+t= 1 x+ay+z+t=b x+y+az+t=b2 x+y+z+at=b3?quotesdbs_dbs6.pdfusesText_11

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