2013-2014第二学期线代期中试卷答案

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(α??1,α??2,α??3,α??4)ÚB

=

(α??3,2α??2,3α??1,4α??4)"®?1??ª|A|=1§¦1??ª|A?B|")µ

|A?B|=|(α??1?α??3,?α??2,α??3?3α??1,?3α??4)|

=?6|(α??1,α??2,α??3,α??4)|=?6

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2.®?Ý??A=??1200?

???0024??§¦An"???0002

)µAn=An

?? ??

100An§Ù¥A2424

1=2

??12§A2

=0224 ??2n2n2n?1

An1=4n?1A1=4n?1n12§A2=

02n

3. 4??1??ªD¥111????1§2§0§-4§121?????{fª?6§x§19§2§¦x")µÏ?a11A31+a12A32+a13A33+a14A34=0,

k1×6+2×(?x)+0×19+(?4)×(?2)=0¤±x=7

1??(??o?)??4.e????? ¤k???þ??K¢ê§…???????Úþ?1§KT???¡?‘ÅÝ??"~Xµ0.10.2

0.90.8

=?2??‘ÅÝ??"y AÚB?n??‘ÅÝ??.y²µAB?´‘ÅÝ??"

)µ A=(aij)n×n§B=(bij)n×n§AB=(cij)n×n.dA§B?‘=Ý????§é?¿1≤j≤nk

??naij=1,

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i=1

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??n??nncij=

??naikbkj

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i=1k=1

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k=1

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¤±`²àg?5?§|(A?B)X=0?k")§ r(A?B)=5.

??.(10©) ?5?§|

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???a11x1

+a12x2+···+a1nxn=b1,.?.?.?

an1x1+an2x2+···+annxn=bn.

k??)§??Øe???§|??)???¹"

??????a11x1+a21x2+···+an?1,1xn?1=an1,?...?????a1nx1+a2nx2+···+an?1,nxn?1=ann,?b1x1

+b2x2

+···bn?1xn?1

=bn

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)µ1???§|k??)`²r(A)=n§=XêÝ????¤k???þ?5Ã'§

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n.(12©)¦e??1??ª???µ

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)µ)µ

????????122+xy3+xyz????????????1x+1x+y+xyx+y+z+xyz????????????1x2+1x2+y2+xyx2+y2+z2+xyz??????????1??x3+1x3+y3+xyx3+y33??????????+z+xyz????1123??

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=????1xx+yx+y+z????

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????1x3x3+y3333????

??????x+y+z??

??1111??

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=????1xyz????

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????1x2y2z2????

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??1x3y3z3??????

=(x?1)(y?1)(z?1)(y?x)(z?x)(z?y)

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£2¤??b=2§a=1?§β?±dα1§α2§α3??L«§β=?α1+2α2¶

??b=2§a=1?§β?±dα1§α2§α3?5L«§β=?(2k+1)α1+(k+2)α2+kα3"

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