用Matlab学习线性代数 - 线性方程组与矩阵代数概要(5)

>> g=inv(A')*inv(B'); >> h=(inv(A)*inv(B))'; >> c-d ans =

-3.9602e+001 1.5266e+001 1.0821e+001 1.3845e+001 -1.4016e+001 1.5778e+001 1.4313e+000 -5.5182e-001 1.4537e+001 -1.9398e+001 -2.7296e+001 2.6289e+001 2.2261e+001 -3.9304e+001 -4.8956e+001 5.1120e+001 >> c-g ans =

-1.6875e-014 -5.4712e-013 -1.3216e-012 1.5774e-012 -2.8866e-015 -1.3145e-013 -3.1264e-013 3.7659e-013 8.8818e-015 2.6290e-013 6.3949e-013 -7.6028e-013 2.5757e-014 7.1765e-013 1.7195e-012 -2.0606e-012 >> c-h

ans =

-3.9602e+001 1.5266e+001 1.0821e+001 1.3845e+001 -1.4016e+001 1.5778e+001 1.4313e+000 -5.5182e-001 1.4537e+001 -1.9398e+001 -2.7296e+001 2.6289e+001 2.2261e+001 -3.9304e+001 -4.8956e+001 5.1120e+001 >> d-g ans =

3.9602e+001 -1.5266e+001 -1.0821e+001 -1.3845e+001 1.4016e+001 -1.5778e+001 -1.4313e+000 5.5182e-001 -1.4537e+001 1.9398e+001 2.7296e+001 -2.6289e+001 -2.2261e+001 3.9304e+001 4.8956e+001 -5.1120e+001 >> d-h ans =

-2.4158e-013 -1.1724e-013 -2.7711e-013 5.2580e-013 -5.6843e-014 -1.8652e-014 -5.3291e-014 1.0658e-013

4.2633e-014 1.7764e-014 4.7962e-014 -8.8818e-014 1.5987e-013 6.7502e-014 1.8474e-013 -3.3396e-013 >> g-h ans =

-3.9602e+001 1.5266e+001 1.0821e+001 1.3845e+001 -1.4016e+001 1.5778e+001 1.4313e+000 -5.5182e-001 1.4537e+001 -1.9398e+001 -2.7296e+001 2.6289e+001 2.2261e+001 -3.9304e+001 -4.8956e+001 5.1120e+001 >> 第二题： （1） >> n=200;

>> A=floor(10*rand(n)); >> b=sum(A')'; >> z=ones(n,1); >> c=linsolve(A,b);

>> d=c-z；精度为 1e-14-----1e-13;

tic,x=A\\b,toc = Elapsed time is 0.016000 seconds.

tic,inv(A)*b,toc = Elapsed time is 0.031000 seconds. （2） n=500;

>> tic,x=A\\b;toc

Elapsed time is 0.187000 seconds. >> tic,y=inv(A)*b;toc

Elapsed time is 0.343000 seconds.

>> max(abs(x-z))=4.3987e-013 >> max(abs(y-z)) = 2.2524e-012 >>

>> n=1000; >> tic,x=A\\b;toc

Elapsed time is 0.920000 seconds. >> tic,y=inv(A)*b;toc

Elapsed time is 1.404000 seconds.

>> max(abs(x-z)) =1.8221e-012 >> max(abs(y-z)) =2.0862e-011 >> （3）

>> A=floor(10*rand(6)); >>B=A’;

更快！ 更精确！ 更快！ 更精确！ >> A(:,6)=-sum(B(1:5,:))' A =

0 6 7 7 0 -20 5 8 4 7 0 -24 6 7 4 3 3 -23 8 5 1 8 7 3

>> x=ones(6,1); >> b=A*x b = 0 0 0 0 0 0

>> det(A)= 0 >> rref(A)

8 3 3 9 2 8 3 -27 4 -25 8 -28