線性代數(shù) (陳建龍 著) 科學(xué)出版社 課后答案.pdf

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1、線性代數(shù)陳建龍版課后習(xí)題答案摘自：張小向，陳建龍，《線性代數(shù)學(xué)習(xí)指導(dǎo)》(ISBN:978-7-03-021177-4),科學(xué)出版社,2008年3月。習(xí)題1(A)一.填空題??11/21/31.?110?.2.3212n?1??/3.3.O.????201?????33/21???2100??11/20??3/2?1/2004.??.5.???1/210.6.?1.0032???????002??005/23?/2?17.E+A.8.40.9.abcd.??1100?1??0110?10.?1/70.11.(2A+E).12.??.30011???????0001???1/20

2、013.?010?.14.0.15.1.??????101/2?xyy112=???11?16.2.17.?3.18.?,??.?x=?+yy2???12212二.選擇題1.C.2.D.3.B.4.A.5.C.6.C.7.D.8.D.9.B.10.C.11.C.12.A.13.C.14.B.15.C.16.D.17.B.18.D.1習(xí)題1(B)??6112???21322??058?1019?1.??113?,??.2.????21720,??056?.????1466??73????4292?????290?xz=?65?+zz,11239999????23???24ii3

3、43.?xzzz2123=?+1227,4.4,??,??10099.????46???46i4?x=?10zzz?5+20.3123??35??da11da12da13????5.(1)6.(2)(068).(3)dbdbdb.????212223??49??dcdcdc????313233??ad11ad22ad33n??(4)??bd11bd22bd33.(5)∑axxijij.??ij,1=cdcdcd??112233123??010??010??010??001??010??????????(6)001=001,001=000,001=O,?????????????

4、?000????000????000????000????000n??010??當(dāng)n>3時(shí),001=O.????000????nn??12nn(1?)nn??4000λλn2λ????0400(7)0λλnnn?1.(8)??.????0040??00λn??????0004??00??6.02.7.都不成立????12???01??10??10??00???008.(1)??.(2)??.(3)A=??,X=??,Y=??.??00??00??00??00??012??10(4)??.??01?TTTTTT9.(1)(AA)=(A)A=AA.T(2)提示:設(shè)A=(aij)m

5、×n,考察AA的主對(duì)角線元素.T10.提示:比較(AB)與AB.??100??abc??00011.提示:令A(yù)=??012,B=?uvw?滿足AB=BA.再令C=??002,????????312??xyz??311AB=BA?CB=BC.從而推得一切與矩陣A可交換的矩陣如下:??1????+uyz003????uy?+z2y????3yyz其中u,y,z為任意常數(shù).??1010??10100???????00120101100?12.??.13.??.14.??.??00?2433???00010??????3131??00001??100??15.010.????001?

6、???100??103???120??100??123???????????16.010=010010001001.??????????????001????001????001????010????01017.略.???11/21/2??112??/3???21????18.(1)??.(2)??301?.(3)???2/317/9.??3/2?1/2??????11/21/2?????1113??210????51??133?/2??19.(1)??.(2)??.(3)??134?.??30??011?????102????21220.??.??013???1?1?1?1

7、21.(1)X=EX=(AA)X=A(AX)=A(AY)=(AA)Y=EY=Y.?1?1?1?1(2)X=XE=X(AA)=(XA)A=(YA)A=Y(AA)=YE=Y.T?1T?1TT?1TT?1?122.A(A)=(AA)=E=E?(A)=(A)=A.2?1?1?1?1?12?123.A=(PBP)(PBP)=PB(PP)BP=PBEBP=PBP.kk?1依此類推,對(duì)于任意的正整數(shù)k,A=PBP.n設(shè)f(x)=anx+…+a1x+a0,則nn?1?1?1f(A)=anA+…+a1A+a0E=anPB