《高等代数》第二学期期末考试卷参考答案

《高等代数》第二学期期末考试卷参考答案

(

6

32

)

1.(6

)

ξ1,ξ2,ξ3

3

,

Vα

β

α=ξ1+2ξ2 ξ3,β=ξ1 ξ2 ξ3,

α

6;

0;2.(4

)

A=

11

1201

00

20

W

R5

W⊥

W⊥

3;( 1,1,1,0,0),( 1,1,0,0,1),(0,0,0,1,0)

,

3.(4) (α)

V

(β)

α,β

| (α) (β)|=

π

3;

|α β|

4.(4 )2

13; 5.(10

1

,

1

1

,

1

.

1

.

)abc>0,f(x,y,z)=ayz+bzx+cxy

,

=

=

ba

,

2

=

22

a

,

R

C

(B)(α,β)=|a1|+|a2|+|b1|+|b2|;

(D)(α,β)=a1b1+a1b2+a2b1+a2b2;

(A)(α,β)=max{a1,a2,b1,b2};

(C)(α,β)=2a1b1+a1b2+a2b1+2a2b2;

《高等代数》第二学期期末考试卷参考答案

.B

(A)(C)3.

(α,β)=0,α=0β=0;( (α), (α))=(α,α), (α)=α;

(B)

(D)

α=0,(α,α)=0;( (α), (β))=(α,β),

=idV.

.C

(A)A(C)A5.

(B)A(D)A

±1;

n

V

100 0 12 022

(B)

11

B

1

1

1

1

(A)

(12

1

11)

;

1

; (C)

1

; (D)

1

.

1 A= 1

a

1a1

a

1 , 1

β=(1,1, 2)T.AX=β

(1)a(2)QD,QTAQ=D.

(1)AX=βdetA= (a+2)(a 1)2=0,

AX=βr(A)=r(A,β),a 2.

(2)Aλ1=0,λ2=3,λ3= 3,( 1,0,1)T,α3=(1, 2,1)T.α1,α2,α3γ1=

a

2

1.

β

α1=(1,1,1)T,α2=

1

α,γ2= 12α2,γ3=16α3.31

Q=(γ1,γ2,γ3),D=diag{0,3, 3},

QTAQ=D.

2

《高等代数》第二学期期末考试卷参考答案

2.

λ>

√

2y+11

2y

2.f

µi<0(i=1,2,3) λ<

√

2>0,µ3=1

√

22 1 0

0 1

2

0 →

0 1

00

00

λ 1 λ

λ 1

λ λ

λ

1

λ

λ → 0

1

λ

→

012

2.

A

λ

λ<0,

λ

<0

2λ<0,λ<

√

2,2},

f

3

2.

λ>

√

2,µ3=λ+

√

20

2 2

→

0 12

1

(2)(2)

《高等代数》第二学期期末考试卷参考答案

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