数学实验10.6线性代数实验(二).docx

%10.6%第一大题%1.1m=4;A=1 -2 -1 2;-2 4 2 -6;2 -1 0 3;3 3 3 4;AV=rank(A);if m=AV Z=向量组A线性无关else Z=向量组A线性相关endA1=rref(A)%Z =向量组A线性相关A1 = 1.0000 0 0.3333 0 0 1.0000 0.6667 0 0 0 0 1.0000 0 0 0 0%向量组的秩为2；向量组A为线性相关向量组；a1和a2为一个极大无关组；a3=%1.2B=fix(30*rand(6); for i=1:6 if B(i,i)=0 for j=i+1:6 B(j,:)=-B(i,:)*B(j,i)/B(i,i)+B(j,:); end else for k=i+1:6 if B(k,i)=0 C=B(i,:); B(i,:)=B(k,:); B(k,:)=C; break; end end end end B%B = 19.0000 20.0000 10.0000 27.0000 9.0000 14.0000 0 -27.4737 8.2632 -39.7895 9.7368 -16.6316 0 0 16.2050 3.5862 10.5536 5.0651 0 0 0 8.7107 -4.0046 17.0807 0 0 0 0 -14.6511 23.8761 0 0 0 0 0 37.5963%1.3A=1 2 4 6 -3 2;2 4 -4 5 1 -5;3 6 2 0 5 -9;2 3 0 4 0 1;0 -4 -5 2 1 4;5 5 -3 6 6 -4;b=2 ;-1; 3; 4 ;-2; 5;B=A b;R1=rank(A)R2=rank(B)if R1=R2 Z=方程组无解else Z=方程组有解endRR=rref(B)%R1 =5 R2 =5Z =方程组有解RR = 1.0000 0 0 0 0 6.8068 6.6809 0 1.0000 0 0 0 -2.2520 -0.9342 0 0 1.0000 0 0 -0.2041 0.0315 0 0 0 1.0000 0 -1.4644 -1.6397 0 0 0 0 1.0000 -3.1000 -2.3000 0 0 0 0 0 0 0%1.4A8=magic(5)D,X=eig(A8)%A8 = 17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9D = -0.4472 0.0976 -0.6330 0.6780 -0.2619 -0.4472 0.3525 0.5895 0.3223 -0.1732 -0.4472 0.5501 -0.3915 -0.5501 0.3915 -0.4472 -0.3223 0.1732 -0.3525 -0.5895 -0.4472 -0.6780 0.2619 -0.0976 0.6330X = 65.0000 0 0 0 0 0 -21.2768 0 0 0 0 0 -13.1263 0 0 0 0 0 21.2768 0 0 0 0 0 13.1263%1.5A=1 1 -2 -3 0 0 ;1 2 1 4 0 3;-2 1 -1 2 -3 1;-3 4 2 1 -1 2;0 0 -3 -1 -4 4;0 3 1 2 4 -1;D,X=eig(A)P=orth(D)%D = -0.1125 -0.4801 -0.1592 0.5581 -0.5933 0.2609 -0.0548 0.5706 0.1797 0.3749 -0.4021 -0.5805 -0.3665 0.0003 -0.7518 0.2573 0.3826 -0.2966 -0.1251 -0.6457 0.3949 0.0057 0.1740 -0.6175 -0.7539 0.0259 -0.0112 -0.5372 -0.3771 0.0073 0.5158 -0.1627 -0.4703 -0.4394 -0.4093 -0.3545X = -8.3609 0 0 0 0 0 0 -4.2224 0 0 0 0 0 0 -2.1320 0 0 0 0 0 0 0.7192 0 0 0 0 0 0 3.8471 0 0 0 0 0 0 8.1489P = 0.1296 0.7932 0.0522 -0.1125 -0.0015 0.5819 -0.0065 0.2540 0.8375 -0.0548 -0.2123 -0.4311 0.5965 0.2509 -0.3997 -0.3665 -0.1639 -0.5103 0.6024 -0.4672 0.2838 -0.1251 -0.3436 0.4523 -0.4976 -0.0946 -0.0744 -0.7539 -0.3994 0.0998 -0.1299 0.1267 -0.2235 0.5158 -0.8065 -0.0260其标准型为：f=-8.3609*y12 -4.2224*y22-2.1320*y32+0.7192*y42+3.8471*y52+8.1489*y62%第二大题(1)A=3 1;0 5;B=3 9 25 8 0 11 20 7 10 8 7;0 8 20 5 13 8 18 8 0 18 8;C=A*B;C1=rem(C,26)%C1 = 9 9 17 3 13 15 0 3 4 16 3 0 14 22 25 13 14 12 14 0 12 14%明文为：jajorwdznnpoamdoeaqmdo(2)ad=det(A);a1=5 -1;0 3;a2=11*a1+ad*26;a3=rem(a2,26);c1=25