线性代数习题答案.pdf

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1、㓐ড়㒗дϔ01AA.01BBC.ǃ01CA.01DA.01Er=2,s=5,t=8៪r=5,s=8,t=2៪r=8,s=2,t=5.01Fi=2,j=1.01G-12.01Haaaaa;aaaaa;aaaaa.13253142541325324451132534415201Ik2;ᥦ߫ⱘ䗚ᑣ᭄ЎᔧkЎي᭄ᯊ,ᥦ߫Ўيᥦ߫,ᔧkЎ༛᭄ᯊ,ᥦ߫Ў༛ᥦ߫.a11a12a13a14a21a22a23a2401K(1);1(2)-(a11+a22+a33+a44);(3)a31a32a33a34.a41a42a43a44f(x)

2、g(x)s(x)01M48x-18.01NfÅ(x)gÅ(x)sÅ(x).01O-1.fÅÅ(x)gÅÅ(x)sÅÅ(x)02ABD.ǃ02B-3.02C6.02Dx=0,-1,-2.02E()-1n-1(n-1)xn.111n(n-1)nn-1(n+1)02F(++...+n).n!.02G(-1)2.23202H()-1n-1(na-x)xn-1.02I(-1)n[(a-1)n-an].03AB.03BD.03CD.03DD.03E12246000.03Fa=0,b=0.44b03Gê1,ê3.03Haƒi03If

3、(x)=2x2-3x+1.iai=1i=1i03Jx4.03L0.03M0.04A(1-a+a2)(1-a)3.04Bn+1.a1a2an04Cx1x2...xn-1(1+x+x+...+x).12n11104Dx1x2...xn[1+a(x+x+...+x)].12n04E(x-1)n..49.2n04F1+()-1a+()-1aa+...+()-1aa...aa121nn-121n(n-1)aᔧa=b,°04G®bn+1-an+1°ᔧaòb.¯b-a05A0.05B-1.05C12/5.05D0.05E0.05F0

4、.05G(1)0;(2)144.05H-9,18.06An!(n-1)!(n-2)!...2!1!.06B¥(cosj-cosj).ij4ij1207A(1-x)(10-x).08AAB.ǃ08BD.08CCD.ǃ08DD.08Eò2.08Faò0Ϩbò-b/4.08Gf(x)=2x2-3x+1.08H⬆ǃЭǃϭϝ⾡࣪㙹৘䳔3गܟ,5गܟ,15गܟ.㓐ড়㒗дѠ01AB.01BD.01CC.01DC.01ED.01FB.01GD.01HC.01I1/3.01J2.01K0.01La2(a-2n).01N(A+B)(A-B

5、).01S(2)A2+49(A2-E).01T(1)1,(2)n.n+1n+1n+1k01U(1)(-1).(2)(-1)(k=1,2,?,n).2(n-1)!n!01Vϸᑈৢ೼ቫ㘠Ꮉ668Ҏ,෍䆁Ҏਬ334Ҏ.146624801Wे᱈໽ὖ⥛Ў,䰈໽ⱘὖ⥛Ў,ϟ䲼໽ⱘὖ⥛Ў.256256256⊬xn+1·⊬023/2·⊬xn·⊬x4·⊬260·01X∆y¸=∆∆∆1/200¸¸¸∆y¸.∆y¸=∆236¸∆n+1¸∆∆¸¸∆n¸∆4¸∆∆¸¸∆¸∆¸∆¸∆¸«zn+1¹«01/40¹«zn¹«z4¹«22¹⊬01-21

6、·98⊬22·n-1∆∆02-42¸¸⊬∆-222·¸02A4«42¹.02B2∆01-21¸.02C∆¸.∆¸«22-2¹«02-42¹n-1n⊬n(n+1)·⊬2.4400·∆1n2¸∆n-1n-1¸∆¸∆42.400¸02D∆01n¸.02E∆∆nn-1¸¸.∆¸002n.2∆¸∆n¸«001¹«0002¹.50.⊬100·∆¸502FA=∆200¸.⬅ѢA=A.∆¸«6-1-1¹⊬1000·∆¸n+11∆-1200¸03A(1)(-1)A.(2)∆¸.n!0-230∆∆¸¸«00-34¹1-1(3)-A-6E.

7、(4)(E-B).(5)B=-(E-2A).2⊬101·03BB=∆5-10¸.03C(2)A2-A-E.03D-1(A-2E).∆∆¸¸5«-211¹-11-1103EA=(A-3E).(A-4E)=(A+E).106-112-1-1-103FB=-(5A+3A-E).03G(EA+BA)=B(E+AB)B.14-112-1-103HB=(A+3A+4E).03I(E-AB)=E+A(E-BA)B.10⊬1000·∆¸∆-1/21/200¸⊬122·-1∆1∆21-2¸03NA=∆∆∆-1/2-1/61/30¸¸¸0

8、3O∆∆¸¸.∆∆¸¸¸9«2-21¹∆¸«1/8-5/24-1/121/4¹⊬00-201·∆¸∆000-34¸03P∆∆∆0012-3¸¸∆¸∆∆∆3-1000¸¸¸¸«-52000¹⊬(A1-A2A-41A3)-1-A-11A2(A4-A3A-11A2)-1·03Q¸¸.∆∆«-A-41A3(A1-A2A-41A3)-1(A