(線性代數(shù))(A)考卷

1、 /13四、計(jì)算題：（本題滿分分）A,B四、計(jì)算題：（本題滿分分）A,BAIBA2BA8E,得分評閱人,A為AAb|0H0E011得分評閱人五、解答題：（本題滿分分）xx3TOC o 1-5 h z.123xMXx123IXX喙1123七、解答和證明題:（每小題分，共分）10B00B1ABJ10副口B30a,.03GV0X.得分評閱人n1DDDDDD1、設(shè)A為4DDDDA=20|A*2、設(shè)A是4DDDDDDDDD1,則addddddd3DDDDf=x2+4x2+4x2+2txxIExx+4xx000000004、13DDDADDE*|=0,|2E*|=0,3E*|=01則5DDDDDDDDxi

2、+x2+x3+x4=00DDDDDDDDDDD0DDD6、口nDODA0DDDDDDDD0,且R(A)=nlttDDDDDDDAX=007、口口組l=(1,2,3)tD=(2,3,4)t,=(3,4,5)t01為8、口口口=(1,1,2)t與口、口口nDDDDODDDDDDDDDDD(l)DDDDD0口、口A=22DDDDDODODODDaxxxxaxxxxaxxxxa=(,IE,)t0口，D二xkx41123lxkxxk21口2B4:31A為nDODOD232x*3(3)DDDDDDDDDDODDD10A=213210151DDDDDDDD?DDDDDDDDDDDDPuAPDDDOD,DDD

3、ODA*0DD0D0D6.k(1,1,.T,kDQQDQ7.28.arccos(-6)fcrccos56a(n1)xxxxa(n1)xxxx口、D=a(n1)xaxx=0ax00a(n1)xxax00ax0a(n1)xxxa000ax口、口口,口4.1/6Et1l.82.03.5.3=a+(n)x(alk)nHB=(A,b)=kk2(k1)(4k)當(dāng)當(dāng)ku且k=HkI2R(A)=R(B)=3,HHHH；R(A)=2R(B)=3HWH當(dāng)k=4時(shí)，x134x2341H0：8!b!10.0(v印1:X=+kAaaaaaa:48k(k4)0R(A)=R(B)=23,HHHH1013(kHR)|，*|二

4、)(BB6)=0AQQQDD：=1,=6,:,=1,對應(yīng)的1次線性方程組為：(E)X=02I22一=Bn1011=11124JX04I2:0:11=62=BB3P=(,)=1|A|=2-Aqqpap=A=BE,a=10,a=7,A11A*Ah=3121321=2,4IE,a=ie,23a=*,31AJ，A33=11221221323A31.=2A|I52321A:733|212112(A*)tA*=(|A|Ah)t|A|Ah=|A|2(At)hAh=|A|2(AAt)hAAt=E-|AAt|=|E|-|A|2=11(a*)tA*=Eh=E一、1、D=01050226330704082、設(shè)二(2

5、,3,5),=(3,7,8),=(1,IE,1)，若3、設(shè)A為三階可逆矩陣，且3巨A=電4、若n階方陣A有一個(gè)特征值2,則2312營則0112E*|二5、如果二次型范圍是f(x,x,x)=x2+x2+5x2+2txxRxx+4xx是正定的，則t的取值31231213二、1、若齊次線性方程組kxxx0123|xkxx0僅有零解，則.123觸xxx0(A)k=4或k=(B)123k=*或k=1(C)k*且k(D)k且k12(A)都不是零向量2)線性無關(guān)的充分必要條件是任意兩個(gè)向量的分量不成比例(C)至少有一個(gè)向量不可由其余向量線性表示(D)每一個(gè)向量均不由其余向量線性表示3、A,B均為n階方陣，下

6、列各式中成立的是(A)(A+B)2=A2+2AB+B2(B)(C)設(shè)AB=0,則A=0或B=0(D)若|A+AB|=0,則A|=0或|E+B|=04、設(shè)n階方陣A的秩rn,則在A的n個(gè)行向量中(A)必有r個(gè)行向量線性無關(guān)(B)任意r個(gè)行向量均可構(gòu)成最大無關(guān)組(C)任意r個(gè)行向量均線性無關(guān)(D)任一行向量均可由其它r個(gè)行向量線性表示5、n階方陣A可與對角矩陣相似的充分必要條件是(A)A有nDDDDDDDDDD(B)A有nDDDDDDD(C)A的nDDDDDDDD(D)A有nDDDDDDD三口三口1、設(shè)A為4DDDD112、計(jì)口nDDDDD二.A|=1DD311103A*An01113DDDDDD

7、l=(1,1,1,1),11=(1,*,1,),B3=(1,3,1,3),.=(1,嘰，1)(1)Dl，II-(2)DDDDDDDDDDDDDDDD10X31a10X31a,bDDDDDDDDDDDDDDD4、設(shè)AX+B=XD其中A=,111JJB=J101|xxxx1.12345DDDDDDx2-x3x42DD7x2x2x4xa1234xxx5xb1234DDD110B-006DDDDDA二10JB=,30熱003|鼻0 xI(1)Dx(2)DDDDDPD使PnAP=Baaaa13a件:23a.33AJaijDDDDDDD(2)a111c7D0000f(x,x,x)=x2+2xx+2xx+2x2+4xxDDOODOOODDDOOTOC o 1-5 h z線性變換12311213223aaDDDDDDDA=工a1