《线性代数》机考试卷考试答案.docx

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1、(c)(机考部分，共30分)开课系部：基础部,考试时间：辿_年上月日考试形式：闭卷口、开卷,允许带 入场考生姓名：学号：专业：班级：题序12345678总分得分评卷人1110l(x) = 3x6 + 4x43x3-15x-812，试求：解: A=ll 2 7 2 6;2 6 6 1 10;9 4 1 6 3;8 9 5 9 2;4 2 9 8 12A =1129842649276159216986103212 a=det(A)a =-42305 Al=inv(A)Al =0.0694-0.03720.1066-0.0730-0.01420.1040-0.0538-0.07940.0720-0.

2、0045-0.22590.0394-0.03000.06950.10590.0322-0.0359-0.07850.03040.0874-0.0482 0.0807 0.1199 -0.1024 0.0273(2) f=3*AA6+4*AA4+3*AA3-15*A-8*eye(5)B =419873642391152262353954782486276900558132909249630154233368490210651578289702065332350010338097780315427512285137333391863148450069039310243024289497867261

3、893698360215775413217394389313683363438283328323849451236690518669929-9,B 二12-610-521 detA9detB) AB+A Ir+AB 1 + E解:a=5 8 6 19;2 4-4 3 13;4 739 -9;12 6 8 2 5;1 5 9 10 3A =-5 8 6 1 924-43134739-912 -6 8 2 5159103 B=-5 15 15 -6;6 5 4 -12 14;2 9-6 3 -6;9 7 3 8 4;8 -5 6 21 9B =-5 15 15 -6654-121429-63-69

4、73848 -56 21 9 det(A),det(B)ans =191040ans =159466(2) C=A* B,+AB+AB+eye(5)C =25.8638 -102.9093 -26.9937 74.0866 54.6565-60.3036 -199.9423 -5.7090 110.4054 149.1000191.2367 89.2569 135.7324 132.3916 124.0444-25.0780 -20.8033 -101.9129 127.5072 263.4305178.1519 -95.3682 4.6975 164.3786 274.2461 A=-5 8

5、 6 1 9;2 4 -4 3 13;4 739 -9;12 -6 8 2 5;1 5 9 10 3-5 8 6 1 924-43134739-912 -6 8 2 5159103 B=-5 15 15 -6;6 5 4 -12 14;2 9-6 3 -6;9 7 3 84;8-5 6 21 9-5 16 52 99 78 -55 15 -64 -12 14-6 3 -63 8 46 21 9 C=A*B,+inv(A)*B+A*inv(B)+eye(5)C =26.6420 151.9764 -24.2160 69.9625 57.7470-59.5761 166.7552 -3.1124

6、106.5502 151.7155190.8499 -164.1771 134.3520 134.4411 121.1271-25.6537 117.0622 -103.9675 130.5577 262.7031178.3192 -10.7479 5.2946 163.4920 275.8381(1)A的秩；写出向组A的最大无关组;用该最大无关组表出向量组中的其余向量. A=9 12 15;1542 1;5 993 2;43 55 151219121154259934355r=rank(A)(2) Al=rref(A)Al =0 0.67010 0.79730 -1.01371.000000

7、0 1.0000000 1.0000000 1.0000 0.1993最大无关组为产1，2,即,4表出为产 5 = U6701 + 07973-l0137G+(L19934求:解。解:4 、( 6分)设线性方程组为AX =力(1)化B=(A,b)为行最简形;(2)相应齐次线性方程组的一个础解系；(3)Ax =力通A=8 2 6-1 5 6;4 5-12 2 7;1 3-2 4 1 5;3 4-1-2 1 28 2 645-113-23 4-1-15 62 2 74 15-2 12 b=2;5;l;4b =2514 B=A b826-156245-1227513-241513 4-1-2124

8、Bl=rref(B)Bl =1.00000 1.000000 2.1250 3.37500 1.0000 -1.00000000000 1.00000 1.2083 0.62500000 1.0000 -1.9583 -4.8750基础解系A1=A(i42A5)8 2-154 5 2 213 4 13 4-21Al =826-15645-122713-24153 4-1-212 Bl=null(Al)Bl =-0.6658 0.32510.0353 -0.62130.0353 -0.6213-0.3585 -0.16840.5811 0.27290.2967 0.1394通解为y=y0+11+

9、22+34+45 Vllk2343.375000.625-4.875002 112 1A =12 2112 12125、 (6分)设 A(1,:),A(2,:)=A(2,:)-2*A(1,:)A =12 12 22 112 112 2 110 0 1-11A =12 12 22112 100 1-1-100 1-11A =12 12 20 -3 -1 -2 -30 0 1-1-10 0 1-11 A(2)=A(2,:)/(-3),A(l)= A(1)-2*A(2)1.0000 2.0000 1.0000 2.0000 2.00000 1,0000 0.3333 0.6667 1.000000

10、1.0000 -1.0000 -1.000000 1.0000 -1.0000 1.0000A =1.00000 0.3333 0.666700 1.0000 0.3333 0.6667 1.000000 1.0000 -1.0000 -1.000000 1.0000 -1.0000 1.0000 A(4,:)=A(4,:)A(3,:),A(1,:)=A(1,:)(1/3)*A(3,:),A(2,:)=A(2,：H1/3)*A(3,:)A =1.00000 0.3333 0.666700 1.0000 0.3333 0.6667 1.000000 1.0000 -1.0000 -1.00000

11、000 2.0000A =1.00000 0.0000 1.0000 0.33330 1.0000 0.3333 0.6667 1.000000 1.0000 -1.0000 -1.00000000 2.0000A =1.00000 0.0000 1.0000 0.33330 1.00000 1.0000 1.333300 1.0000 -1.0000 -1.00000000 2.0000 A(1)=A(1)-A(4)3A =1.00000 0.0000 1.000000 1.00000 1.0000 1.333300 1.0000 -1.0000 -1.00000000 1.0000A(2)=A(2)-A(4)*(43)A =1.00000 0.0000 1.00000 1.00000 1.0000000 1.0000 -1.0000 -1.00000000 1.0000 A(3,:)=A(3,:)+A(4,:)A =1.00000 0.0000 1.000000 1.00000 1.0000000 1.0000 -1.000000000 1.0000