大连理工大学线性代数上机作业PPT

软1414 叶秀云201492015 上机报告上机作业一Trial>> A=round(5*rand(5))B=round(5*rand(5))C=round(5*rand(5))b=round(5*rand(5,1))A+BA-BA*B+B*Ainv(A)*binv(A)rank(A)det(B)inv(B)rank(B)inv(A*B)rank(A*B)(B')*(A')inv(A*B)inv(B)*inv(A)inv(A)*C*inv(B)A =4 0 1 1 35 1 5 2 01 3 5 5 45 5 2 4 53 545 3B =4 4 4 2 24 0 3 2 22 1 2 4 33 0 54 41 0 0 1 4C =1 2 4 5 43 5 1 3 13 2 3 1 41 3 3 1 11 1 4 1 5b =21132ans =8 4 5 3 59 1 8 4 23 4 7 9 78 5 7 8 94 5 4 6 7 ans =0 -4 -3 -1 11 12 0 -2-1 2 3 1 12 5 -3 0 12 5 4 4 -1 ans =80 53 79 69 7175 54 74 77 7589 51 85 97 102110 77 111 113 12379 41 79 80 80ans =0.4754-0.3197-0.59840.9672-0.0902ans =0.3197 -0.0164 -0.2541 -0.2049 0.3607-0.8443 0.2869 0.1967 0.8361 -0.8115 -0.7213 0.4344 0.4836 0.6803 -1.05741.4262 -0.6885 -0.6721 -1.60662.1475-0.3279 0.1066 0.4016 0.5820 -0.8443 ans =5ans =418.0000ans =-0.0144 0.4354 0.0574 -0.2727 0.01910.2321 -0.2057 0.0718 -0.0909 0.02390.0718 -0.1770 -0.2871 0.3636 -0.0957-0.1100 0.0048 0.4402 -0.0909 -0.18660.0311 -0.1100 -0.1244 0.0909 0.2919 ans =5ans =-0.8088 0.3399 0.3081 0.8553 -1.02110.0586 0.0335 0.0060 -0.0108 -0.04070.9295 -0.4372 -0.4747 -0.9979 1.3348-0.4252 0.2371 0.2279 0.3635 -0.54670.2265 -0.1176 -0.0336 -0.1592 0.1809 ans =5ans =24 40 45 61 5817 25 9 22 1623 43 48 59 6019 40 52 49 5527 35 59 62 60ans =-0.8088 0.3399 0.3081 0.8553 -1.02110.0586 0.0335 0.0060 -0.0108 -0.04070.9295 -0.4372 -0.4747 -0.9979 1.3348-0.4252 0.2371 0.2279 0.3635 -0.54670.2265 -0.1176 -0.0336 -0.1592 0.1809 ans =-0.8088 0.3399 0.3081 0.8553 -1.02110.0586 0.0335 0.0060 -0.0108 -0.04070.9295 -0.4372 -0.4747 -0.9979 1.3348-0.4252 0.2371 0.2279 0.3635 -0.54670.2265 -0.1176 -0.0336 -0.1592 0.1809 ans =-0.0497 -0.5353 -0.0060 0.6289 0.12910.3583 1.0632 0.4029 -1.7332 -0.66080.4518 1.2872 0.8731 -2.1207 -0.6844-0.7394 -2.4091 -1.6491 4.0507 1.62510.2658 0.7208 0.5187 -1.1788 -0.5129 Trial>>上机作业二Trial>> A=rand(4)B=rand(4)C=rand(4)D=rand(4)Z=[A,B;C,D]det(Z)det(A*D-C*B)A=diag([rand rand rand rand])C=diag([rand rand rand rand])Z=[A,B;C,D]det(Z)det(A*D-C*B)A =0.9027 0.3377 0.7803 0.09650.9448 0.9001 0.3897 0.13200.4909 0.3692 0.2417 0.94210.4893 0.1112 0.4039 0.9561B =0.5752 0.8212 0.6491 0.54700.0598 0.0154 0.7317 0.29630.2348 0.0430 0.6477 0.74470.3532 0.1690 0.4509 0.1890C =0.6868 0.7802 0.4868 0.50850.1835 0.0811 0.4359 0.51080.3685 0.9294 0.4468 0.81760.6256 0.7757 0.3063 0.7948D =0.6443 0.3507 0.6225 0.47090.3786 0.9390 0.5870 0.23050.8116 0.8759 0.2077 0.84430.5328 0.5502 0.3012 0.1948Z =0.9027 0.3377 0.7803 0.0965 0.5752 0.8212 0.6491 0.54700.9448 0.9001 0.3897 0.1320 0.0598 0.0154 0.7317 0.29630.4909 0.3692 0.2417 0.9421 0.2348 0.0430 0.6477 0.74470.4893 0.1112 0.4039 0.9561 0.3532 0.1690 0.4509 0.18900.6868 0.7802 0.4868 0.5085 0.6443 0.3507 0.6225 0.47090.1835 0.0811 0.4359 0.5108 0.3786 0.9390 0.5870 0.23050.3685 0.9294 0.4468 0.8176 0.8116 0.8759 0.2077 0.84430.6256 0.7757 0.3063 0.7948 0.5328 0.5502 0.3012 0.1948 ans =-0.0232ans =0.0161A =0.2259 0 0 00 0.1707 0 00 0 0.2277 00 0 0 0.4357C =0.3111 0 0 00 0.9234 0 00 0 0.4302 00 0 0 0.1848Z =0.2259 0 0 0 0.5752 0.8212 0.6491 0.54700 0.1707 0 0 0.0598 0.0154 0.7317 0.29630 0 0.2277 0 0.2348 0.0430 0.6477 0.74470 0 0 0.4357 0.3532 0.1690 0.4509 0.18900.3111 0 0 0 0.6443 0.3507 0.6225 0.47090 0.9234 0 0 0.3786 0.9390 0.5870 0.23050 0 0.4302 0 0.8116 0.8759 0.2077 0.84430 0 0 0.1848 0.5328 0.5502 0.3012 0.1948 ans =7.3868e-04ans =7.3868e-04Trial>>上机作业三N=201492015;a=15;b=49;c=01;d=41;e=21;f=95;g=45;Trial>> h=90;Trial>> A=[a,b,c,d,3,4;1,2,3,4,4,3;12,15,22,17,5,7;e,f,g,h,8,0]; Trial>> B=rref(A)B =1.0000 0 0 0 0.4130 0.95680 1.0000 0 0 -1.7984 -1.49040 0 1.0000 0 -0.3796 -0.37590 0 0 1.0000 2.0806 1.5380N=201492015;a=15;b=49;c=01;d=41;e=21;f=95;g=45;Trial>> h=90;Trial>> A=[a,b,c,d,3,4;1,2,3,4,4,3;12,15,22,17,5,7;e,f,g,h,8,0]; Trial>> B=rref(A)B =1.0000 0 0 0 0.4130 0.95680 1.0000 0 0 -1.7984 -1.49040 0 1.0000 0 -0.3796 -0.37590 0 0 1.0000 2.0806 1.5380上机作业四Trial>> b1=[1,1.9,f,c];Trial>> b2=[1,1.8,f,c];Trial>> A1=[a,b,c,d;0.5,1,1.5,2;12,15,22,17;e,f,g,h];Trial>> A2=[a,b,c,d;0.3,0.6,0.9,1.2;12,15,22,17;e,f,g,h];Trial>> A3=[a,b,c,d;0.1,0.2,0.3,0.4;12,15,22,17;e,f,g,h];Trial>> A4=[a,b,c,d;0.05,0.1,0.15,0.2;12,15,22,17;e,f,g,h];Trial>> x1=A1/b1 x1 =0.02700.01630.23780.5057 Trial>> x2=A2/b1 x2 =0.02700.00980.23780.5057 Trial>> x3=A4/b1 x3 =0.02700.00160.23780.5057 Trial>> x4=A4/b1 x4 =0.02700.00160.23780.5057 Trial>> x5=A1/b2 x5 =0.02650.01630.23760.5046Trial>> x6=A2/b2x6 =0.02650.00980.23760.5046Trial>> x7=A3/b2x7 =0.02650.00330.23760.5046Trial>> x8=A4/b2x8 =0.02650.00160.23760.5046Trial>>上机作业五a1=rand(5,1)a2=rand(5,1)a3=rand(5,1)a4=rand(5,1)a5=rand(5,1)A=[a1,a2,a3,a4,a5]orth(A)a1 =0.90490.97970.43890.11110.2581 a2 =0.40870.59490.26220.60280.7112 a3 =0.22170.11740.29670.31880.4242 a4 =0.50790.08550.26250.80100.0292 a5 =0.92890.73030.48860.57850.2373A =0.9049 0.4087 0.2217 0.5079 0.92890.9797 0.5949 0.1174 0.0855 0.73030.4389 0.2622 0.2967 0.2625 0.48860.1111 0.6028 0.3188 0.8010 0.57850.2581 0.7112 0.4242 0.0292 0.2373 ans =-0.5932 -0.1881 -0.4330 0.1909 -0.6235 -0.5319 -0.5286 0.1934 -0.5094 0.3752 -0.3288 0.0079 -0.0670 0.7395 0.5835 -0.4137 0.8042 -0.1828 -0.3450 0.1723 -0.2931 0.1960 0.8586 0.1953 -0.3167Trial>>上机作业六Trial>> A=rand(5)eig(A)[d,v]=eig(A)x=rand(5,1)eig(x*x')A =0.4588 0.4889 0.9880 0.0987 0.72120.9631 0.6241 0.0377 0.2619 0.10680.5468 0.6791 0.8852 0.3354 0.65380.5211 0.3955 0.9133 0.6797 0.49420.2316 0.3674 0.7962 0.1366 0.7791 ans =2.6238 + 0.0000i0.0391 + 0.2666i0.0391 - 0.2666i0.2420 + 0.0000i0.4829 + 0.0000id =-0.4582 + 0.0000i -0.4322 + 0.1366i -0.4322 - 0.1366i 0.1428 + 0.0000i 0.2020 + 0.0000i-0.3197 + 0.0000i 0.7401 + 0.0000i 0.7401 + 0.0000i -0.6192 + 0.0000i 0.3539 + 0.0000i-0.5143 + 0.0000i -0.0341 - 0.3116i -0.0341 + 0.3116i -0.2603 + 0.0000i -0.0520 + 0.0000i-0.5266 + 0.0000i 0.0473 + 0.2327i 0.0473 - 0.2327i 0.1237 + 0.0000i -0.9110 + 0.0000i-0.3821 + 0.0000i -0.2604 + 0.1558i -0.2604 - 0.1558i 0.7164 + 0.0000i -0.0373 + 0.0000iv =2.6238 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i0.0000 + 0.0000i 0.0391 + 0.2666i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i0.0000 + 0.0000i 0.0000 + 0.0000i 0.0391 - 0.2666i 0.0000 + 0.0000i 0.0000 + 0.0000i0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.2420 + 0.0000i 0.0000 + 0.0000i0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.4829 + 0.0000i上机作业七A=[1,3/2,0;3/2,-1,1;0,1,1]rref(A)eig(A)B=[1,0,2;0,-1,-2;2,-2,0]rref(B)eig(B)A =1.0000 1.5000 01.5000 -1.0000 1.00000 1.0000 1.0000ans =1 0 00 1 00 0 1ans =-2.06161.00002.0616B =1 0 20 -1 -22 -2 0ans =1 0 20 1 20 0 0ans =-3.0000-0.00003.0000Trial>>上机作业八Trial>> A=[0.7,0.2,0.1;0.2,0.7,0.1;0.1,0.1,0.8]P0=[15;9;6]A =0.7000 0.2000 0.10000.2000 0.7000 0.10000.1000 0.1000 0.8000 P0 =1596Trial>> A*P0ans =12.90009.90007.2000Trial>> A*A*P0ans =11.730010.23008.0400Trial>> A*A*A*A*A*P0ans =10.429910.24249.3277Trial>>。

第一题Lagrange插值函数function y=lagrange(x0,y0,x);n=length(x0);m=length(x);for i=1:mz=x(i);s=0.0;for k=1:np=1.0;for j=1:nif j~=kp=p*(z-x0(j))/(x0(k)-x0(j));endends=p*y0(k)+s;endy(i)=s;endx0=[1:10];y0=[67.052,68.008,69.803,72.024,73.400,72.063,74.669,74.487,74.065,76 .777];lagrange(x0,y0,17)ans=-1.9516e+12x=[1:0.1:10];x=x';plot(x0,y0,'r');hold onplot(x,y,'k');legend('原函数','拟合函数')拟合图像如下拟合函数出现了龙格现象，运用多项式进行插值拟合时，效果并不好，高次多项式会因为误差的不断累积，导致龙格现象的发生。

第二题function fun =nihe(n)m=[67.052*10^6,68.008*10^6,69.803*10^6,72.024*10^6,73.400*10^6,72.063 *10^6,74.669*10^6,74.487*10^6,74.065*10^6,76.777*10^6];w=[1,2,3,4,5,6,7,8,9,10];d1=0;d2=0;d3=0;y1=polyfit(m,w,1);y2=polyfit(m,w,2);y3=polyfit(m,w,3);y2=poly2sym(s2);y3=poly2sym(s3);y4=poly2sym(s4);f1=subs(y1,17);f2=subs(y2,17);f3=subs(y3,17);for p=1:10;d1=d1+(subs(y1,w(p))-m(p))^2;d2=d2+(subs(y2,w(p))-m(p))^2;d3=d3+(subs(y3,w(p))-m(p))^2;endd1=sqrt(d1);d2=sqrt(d2);d3=sqrt(d3);fun=[f1 f2 f3;d2 d3 d4];return;结果三次函数的均方误差最小，拟合的最好。

大连理工大学优化方法上机作业本页仅作为文档页封面，使用时可以删除This document is for reference only-rar21year.March优化方法上机大作业学院：电子信息与电气工程学部姓名：学号：指导老师：上机大作业（一）%目标函数function f=fun(x)f=100*(x(2)-x(1)^2)^2+(1-x(1))^2;end%目标函数梯度function gf=gfun(x)gf=[-400*x(1)*(x(2)-x(1)^2)-2*(1-x(1));200*(x(2)-x(1)^2)]; End%目标函数Hess矩阵function He=Hess(x)He=[1200*x(1)^2-400*x(2)+2,-400*x(1);-400*x(1), 200;];end%线搜索步长function mk=armijo(xk,dk)beta=0.5; sigma=0.2;m=0; maxm=20;while (m<=maxm)if(fun(xk+beta^m*dk)<=fun(xk)+sigma*beta^m*gfun(xk)'*dk) mk=m; break;endm=m+1;endalpha=beta^mknewxk=xk+alpha*dkfk=fun(xk)newfk=fun(newxk)%最速下降法function [k,x,val]=grad(fun,gfun,x0,epsilon)%功能：梯度法求解无约束优化问题：minf(x)%输入：fun，gfun分别是目标函数及其梯度，x0是初始点，% epsilon为容许误差%输出：k是迭代次数，x，val分别是近似最优点和最优值maxk=5000; %最大迭代次数beta=0.5; sigma=0.4;k=0;while(k<maxk)gk=feval(gfun,x0); %计算梯度dk=-gk; %计算搜索方向if(norm(gk)<epsilon), break;end%检验终止准则m=0;mk=0;while(m<20) %用Armijo搜索步长if(feval(fun,x0+beta^m*dk)<=feval(fun,x0)+sigma*beta^m*gk'*dk) mk=m;break;endm=m+1;endx0=x0+beta^mk*dk;k=k+1;endx=x0;val=feval(fun,x0);>> x0=[0;0];>> [k,x,val]=grad('fun','gfun',x0,1e-4)迭代次数：k =1033x =0.99990.9998val =1.2390e-008%牛顿法x0=[0;0];ep=1e-4;maxk=10;k=0;while(k<maxk)gk=gfun(x0);if(norm(gk)<ep)x=x0miny=fun(x)k0=kbreak;elseH=inv(Hess(x0));x0=x0-H*gk;k=k+1;endendx =1.00001.0000miny =4.9304e-030迭代次数k0 =2%BFGS方法function [k,x,val]=bfgs(fun,gfun,x0,varargin) %功能：梯度法求解无约束优化问题：minf(x)%输入：fun，gfun分别是目标函数及其梯度，x0是初始点，% epsilon为容许误差%输出：k是迭代次数，x，val分别是近似最优点和最优值N=1000;epsilon=1e-4;beta=0.55;sigma=0.4;n=length(x0);Bk=eye(n);k=0;while(k<N)gk=feval(gfun,x0,varargin{:});if(norm(gk)<epsilon), break;enddk=-Bk\gk;m=0;mk=0;while(m<20)newf=feval(fun,x0+beta^m*dk,varargin{:});oldf=feval(fun,x0,varargin{:});if(newf<=oldf+sigma*beta^m*gk'*dk)mk=m;break;endm=m+1;endx=x0+beta^mk*dk;sk=x-x0;yk=feval(gfun,x,varargin{:})-gk;if(yk'*sk>0)Bk=Bk-(Bk*sk*sk'*Bk)/(sk'*Bk*sk)+(yk*yk')/(yk'*sk);endk=k+1;x0=x;endval=feval(fun,x0,varargin{:});>> x0=[0;0];>> [k,x,val]=bfgs('fun','gfun',x0)k =20x =1.00001.0000val =2.2005e-011%共轭梯度法function [k,x,val]=frcg(fun,gfun,x0,epsilon,N)if nargin<5,N=1000;endif nargin<4, epsilon=1e-4;endbeta=0.6;sigma=0.4;n=length(x0);k=0;while(k<N)gk=feval(gfun,x0);itern=k-(n+1)*floor(k/(n+1));itern=itern+1;if(itern==1)dk=-gk;elsebetak=(gk'*gk)/(g0'*g0);dk=-gk+betak*d0; gd=gk'*dk;if(gd>=0),dk=-gk;endendif(norm(gk)<epsilon),break;endm=0;mk=0;while(m<20)if(feval(fun,x0+beta^m*dk)<=feval(fun,x0)+sigma*beta^m*gk'*dk) mk=m;break;endm=m+1;endx=x0+beta^m*dk;g0=gk; d0=dk;x0=x;k=k+1;endval=feval(fun,x);>> x0=[0;0];[k,x,val]=frcg('fun','gfun',x0,1e-4,1000)k =122x =1.00011.0002val =7.2372e-009上机大作业（二）%目标函数function f_x=fun(x)f_x=4*x(1)-x(2)^2-12;%等式约束条件function he=hf(x)he=25-x(1)^2-x(2)^2;end%不等式约束条件function gi_x=gi(x,i)switch icase 1gi_x=10*x(1)-x(1)^2+10*x(2)-x(2)^2-34;case 2gi_x=x(1);case 3gi_x=x(2);otherwiseend%求目标函数的梯度function L_grad=grad(x,lambda,cigma)d_f=[4;2*x(2)];d_g(:,1)=[-2*x(1);-2*x(2)];d_g(:,2)=[10-2*x(1);10-2*x(2)];d_g(:,3)=[1;0];d_g(:,4)=[0;1];L_grad=d_f+(lambda(1)+cigma*hf(x))*d_g(:,1);for i=1:3if lambda(i+1)+cigma*gi(x,i)<0L_grad=L_grad+(lambda(i+1)+cigma*gi(x,i))*d_g(:,i+1);continueendend%增广拉格朗日函数function LA=lag(x,lambda,cee)LA=fun(x)+lambda(1)*hf(x)+0.5*cee*hf(x)^2;for i=1:3LA=LA+1/(2*cee)*(min(0,lambda(i+1)+cee*gi(x,i))^2-lambda(i+1)^2); endfunction xk=BFGS(x0,eps,lambda,cigma)gk=grad(x0,lambda,cigma);res_B=norm(gk);k_B=0;a_=1e-4;rho=0.5;c=1e-4;length_x=length(x0);I=eye(length_x);Hk=I;while res_B>eps&&k_B<=10000dk=-Hk*gk;m=0;while m<=5000if lag(x0+a_*rho^m*dk,lambda,cigma)-lag(x0,lambda,cigma)<=c*a_*rho^m*gk'*dkmk=m;break;endm=m+1;endak=a_*rho^mk;xk=x0+ak*dk;delta=xk-x0;y=grad(xk,lambda,cigma)-gk;Hk=(I-(delta*y')/(delta'*y))*Hk*(I-(y*delta')/(delta'*y))+(delta*delta')/(delta'*y);k_B=k_B+1;x0=xk;gk=y+gk;res_B=norm(gk);end%增广拉格朗日法function val_min=ALM(x0,eps)lambda=zeros(4,1);cigma=5;alpha=10;k=1;res=[abs(hf(x0)),0,0,0];for i=1:3res(1,i+1)=norm(min(gi(x0,i),-lambda(i+1)/cigma)); endres=max(res);while res>eps&&k<1000xk=BFGS(x0,eps,lambda,cigma);lambda(1)=lambda(1)+cigma*hf(xk);for i=1:3lambda(i+1)=lambda(i+1)+min(0,lambda(i+1)+gi(x0,1)); endk=k+1;cigma=alpha*cigma;x0=xk;res=[norm(hf(x0)),0,0,0];for i=1:3res(1,i+1)=norm(min(gi(x0,i),-lambda(i+1)/cigma)); endres=max(res);endval_min=fun(xk);fprintf('k=%d\n',k);fprintf('fmin=%.4f\n',val_min);fprintf('x=[%.4f;%.4f]\n',xk(1),xk(2));>> x0=[0;0];>> val_min=ALM(x0,1e-4)k=10fmin=-31.4003x=[1.0984;4.8779]val_min =-31.4003上机大作业（三）A=[1 1;-1 0;0 -1];n=2;b=[1;0;0];G=[0.5 0;0 2];c=[2 4];cvx_solver sdpt3cvx_beginvariable x(n)minimize (x'*G*x-c*x)subject toA*x<=bcvx_enddisp(x)Status: SolvedOptimal value (cvx_optval): -2.40.40000.6000A=[2 1 1;1 2 3;2 2 1;-1 0 0;0 -1 0;0 0 -1]; n=3;b=[2;5;6;0;0;0];C=[-3 -1 -3];cvx_solver sdpt3cvx_beginvariable x(n)minimize (C*x)subject toA*x<=bcvx_enddisp(x)Status: SolvedOptimal value (cvx_optval): -5.40.20000.00001.600011。

大连理工大学线性代数实验上机报告实验一首先随机生成五阶方阵AA=rand(5)A =0.8147 0.0975 0.1576 0.1419 0.6557 0.9058 0.2785 0.9706 0.4218 0.0357 0.1270 0.5469 0.9572 0.9157 0.8491 0.9134 0.9575 0.4854 0.7922 0.9340 0.6324 0.9649 0.8003 0.9595 0.6787>> B=rand(5)随机生成五阶方阵BB =0.7577 0.7060 0.8235 0.4387 0.4898 0.7431 0.0318 0.6948 0.3816 0.4456 0.3922 0.2769 0.3171 0.7655 0.6463 0.6555 0.0462 0.9502 0.7952 0.7094 0.1712 0.0971 0.0344 0.1869 0.7547>> b=rand(1,5)'随机生成列向量bb =0.27600.67970.65510.16260.1190计算A+B>> A+Bans =1.5725 0.8036 0.9811 0.5806 1.1455 1.6489 0.3103 1.6654 0.8033 0.48130.5192 0.8238 1.2743 1.6813 1.49541.5689 1.0037 1.4356 1.5874 1.6434 0.8035 1.0620 0.8347 1.1464 1.4334 计算A-B>> A-Bans =0.0570 -0.6085 -0.6658 -0.2969 0.1660 0.1627 0.2467 0.2758 0.0402 -0.4099 -0.2652 0.2700 0.6401 0.1502 0.2028 0.2579 0.9113 -0.4648 -0.0030 0.2246 0.4612 0.8678 0.7658 0.7726 -0.0760 计算A*B+B*A>> A*B+B*Aans =3.0288 2.3058 3.1439 2.7276 3.10342.9094 2.19673.0040 3.0737 3.25843.3422 2.1423 3.2104 3.5734 3.90494.1446 2.9794 4.3676 4.2354 4.9170 3.1350 1.7787 3.2289 3.1170 3.2815 求Ax=b的解>> x=A\bx =-0.98502.43963.3124-5.65151.7085验证克莱姆法则>> c=A(:,1)c =0.81470.90580.12700.91340.6324>> d=A(:,2)d =0.09750.5469 0.9575 0.9649>> e=A(:,3)e =0.1576 0.9706 0.9572 0.4854 0.8003>> f=A(:,4)f =0.1419 0.4218 0.91570.9595>> g=A(:,5)g =0.65570.03570.84910.93400.6787>> B1=[b';d';e';f';g']'B1 =0.2760 0.0975 0.1576 0.1419 0.6557 0.6797 0.2785 0.9706 0.4218 0.0357 0.6551 0.5469 0.9572 0.9157 0.8491 0.1626 0.9575 0.4854 0.7922 0.9340 0.1190 0.9649 0.8003 0.9595 0.6787>> B2=[c';b';e';f';g']'B2 =0.8147 0.2760 0.1576 0.1419 0.6557 0.9058 0.6797 0.9706 0.4218 0.0357 0.1270 0.6551 0.9572 0.9157 0.8491 0.9134 0.1626 0.4854 0.7922 0.9340 0.6324 0.1190 0.8003 0.9595 0.6787>> B3=[c';d';b';f';g']'B3 =0.8147 0.0975 0.2760 0.1419 0.6557 0.9058 0.2785 0.6797 0.4218 0.0357 0.1270 0.5469 0.6551 0.9157 0.8491 0.9134 0.9575 0.1626 0.7922 0.9340 0.6324 0.9649 0.1190 0.9595 0.6787>> B4=[c';d';e';b';g']'B4 =0.8147 0.0975 0.1576 0.2760 0.6557 0.9058 0.2785 0.9706 0.6797 0.0357 0.1270 0.5469 0.9572 0.6551 0.8491 0.9134 0.9575 0.4854 0.1626 0.9340 0.6324 0.9649 0.8003 0.1190 0.6787>> B5=[c';d';e';f';b']'B5 =0.8147 0.0975 0.1576 0.1419 0.2760 0.9058 0.2785 0.9706 0.4218 0.6797 0.1270 0.5469 0.9572 0.9157 0.6551 0.9134 0.9575 0.4854 0.7922 0.1626 0.6324 0.9649 0.8003 0.9595 0.1190>> x1=det(B1)/det(A)x1 =-0.9850>> x2=det(B2)/det(A) x2 =2.4396>> x3=det(B3)/det(A) x3 =3.3124>> x4=det(B4)/det(A) x4 =-5.6515>> x5=det(B5)/det(A)x5 =1.7085计算A的行列式>> det(A)ans =-0.0250计算B的行列式>> det(B)ans =0.0647求A的逆>> inv(A)ans =3.1375 -0.8078 -1.8788 -4.21945.1680-8.6076 3.5314 2.8907 13.7204 -14.3665 -6.2824 3.7220 3.6132 10.0084 -12.4190 13.6173 -6.8822 -6.3938 -23.5288 27.5825 -2.5292 1.0729 2.4193 5.8870 -7.2671 求B的逆>> inv(B)ans =-0.4430 3.4997 1.3255 -2.6005 -0.4697 1.4047 -1.1626 0.2422 -0.4475 -0.0119 0.7210 -1.8189 -2.0635 2.4434 0.0765 -0.6122 -0.1837 2.0165 0.0375 -1.2564 0.0384 -0.5157 -0.7370 0.5267 1.7407 求A的秩>> rank(A)ans =5求B的秩>> rank(B)ans =5求A*B的行列式>> det(A*B)ans =-0.0016求A*B的逆>> inv(A*B)ans =-74.0649 35.0433 31.2288 121.5740 -137.3442 6.8291 -1.2718 -2.2922 -8.9951 8.6972 63.9620 -31.4202 -29.5061 -105.6918 122.3246 -9.3196 5.7452 4.6259 11.9660 -15.4028 11.9582 -6.3521 -3.3817 -16.7574 18.6360>> rank(A*B)ans =5>> det(A)*det(B)ans =-0.0016验证 （1）>> (A*B)'ans =0.9569 1.5566 1.6237 2.2732 2.25520.6922 0.9401 0.4969 0.9371 0.80900.9461 1.6492 1.6875 2.3563 2.38000.7507 1.5887 1.8840 1.9421 2.14811.1399 1.52122.2149 2.4545 2.4497()()111,,T T T AB B A AB B A AB BA---==≠>> B'*A'ans =0.9569 1.5566 1.6237 2.2732 2.2552 0.6922 0.9401 0.4969 0.9371 0.8090 0.9461 1.6492 1.6875 2.3563 2.38000.7507 1.5887 1.8840 1.9421 2.14811.1399 1.52122.2149 2.4545 2.4497 （2）>> inv(B)*inv(A)ans =-74.0649 35.0433 31.2288 121.5740 -137.3442 6.8291 -1.2718 -2.2922 -8.9951 8.6972 63.9620 -31.4202 -29.5061 -105.6918 122.3246 -9.3196 5.7452 4.6259 11.9660 -15.4028 11.9582 -6.3521 -3.3817 -16.7574 18.6360 （3）>> A*Bans =0.9569 0.6922 0.9461 0.7507 1.13991.5566 0.9401 1.6492 1.5887 1.52121.6237 0.4969 1.6875 1.88402.21492.2732 0.9371 2.3563 1.9421 2.4545 2.2552 0.8090 2.3800 2.1481 2.4497>> B*Aans =2.0719 1.6135 2.1978 1.9769 1.9635 1.3528 1.2566 1.3549 1.4850 1.7372 1.7186 1.6454 1.5229 1.6894 1.6900 1.8714 2.0423 2.0113 2.2932 2.4625 0.8797 0.9697 0.8489 0.9690 0.8317 求矩阵X使得AXB=C首先随机生成五阶方阵C>> C=rand(5)C =0.4984 0.7513 0.9593 0.8407 0.35000.9597 0.2551 0.5472 0.2543 0.19660.3404 0.5060 0.1386 0.8143 0.25110.5853 0.6991 0.1493 0.2435 0.61600.2238 0.8909 0.2575 0.9293 0.4733X=A 的逆*B 的逆>> X=inv(A)*C*inv(B)X =3.8432 -13.8858 2.1418 9.4404 -4.5871-9.3312 41.9602 -7.9101 -28.4683 14.8942-7.8738 35.1218 -5.4107 -22.8861 10.158116.7545 -75.6079 14.6784 49.3951 -24.7450-3.5568 17.0848 -2.9018 -11.2670 5.4559实验二1. 验证：对于一般的方阵A,B,C,D ，首先随机生成方阵A,B,C,D A=rand(5)A BA DB CC D ≠-A =0.8258 0.1067 0.8687 0.4314 0.1361 0.5383 0.9619 0.0844 0.9106 0.8693 0.9961 0.0046 0.3998 0.1818 0.5797 0.0782 0.7749 0.2599 0.2638 0.5499 0.4427 0.8173 0.8001 0.1455 0.1450>> B=rand(5)B =0.8530 0.0760 0.4173 0.4893 0.7803 0.6221 0.2399 0.0497 0.3377 0.3897 0.3510 0.1233 0.9027 0.9001 0.2417 0.5132 0.1839 0.9448 0.3692 0.4039 0.4018 0.2400 0.4909 0.1112 0.0965>> C=rand(5)C =0.1320 0.2348 0.1690 0.5470 0.1835 0.9421 0.3532 0.6491 0.2963 0.3685 0.9561 0.8212 0.7317 0.7447 0.6256 0.5752 0.0154 0.6477 0.1890 0.7802 0.0598 0.0430 0.4509 0.6868 0.0811>> D=rand(5)D =0.9294 0.3063 0.6443 0.9390 0.2077 0.7757 0.5085 0.3786 0.8759 0.3012 0.4868 0.5108 0.8116 0.5502 0.4709 0.4359 0.8176 0.5328 0.6225 0.2305 0.4468 0.7948 0.3507 0.5870 0.8443>> Z=[A,B;C,D]Z =0.8258 0.1067 0.8687 0.4314 0.13610.8530 0.0760 0.4173 0.4893 0.78030.5383 0.9619 0.0844 0.9106 0.86930.6221 0.2399 0.0497 0.3377 0.38970.9961 0.0046 0.3998 0.1818 0.57970.3510 0.1233 0.9027 0.9001 0.24170.0782 0.7749 0.2599 0.2638 0.54990.5132 0.1839 0.9448 0.3692 0.40390.4427 0.8173 0.8001 0.1455 0.14500.4018 0.2400 0.4909 0.1112 0.09650.1320 0.2348 0.1690 0.5470 0.18350.9294 0.3063 0.6443 0.9390 0.20770.9421 0.3532 0.6491 0.2963 0.36850.7757 0.5085 0.3786 0.8759 0.30120.9561 0.8212 0.7317 0.7447 0.62560.4868 0.5108 0.8116 0.5502 0.47090.5752 0.0154 0.6477 0.1890 0.78020.4359 0.8176 0.5328 0.6225 0.23050.0598 0.0430 0.4509 0.6868 0.08110.4468 0.7948 0.3507 0.5870 0.8443求Z的行列式>> det(Z)ans =-0.0295求det(A)*det(D)-det(B)*det(C)>> det(A)*det(D)-det(B)*det(C)ans =1.8656e-004随机生成对角矩阵A>> A=diag([rand rand rand rand rand])A =0.1948 0 0 0 0 0 0.2259 0 0 0 0 0 0.1707 0 0 0 0 0 0.2277 0 0 0 0 0 0.4357 随机生成对角矩阵B>> B=diag([rand rand rand rand rand])B =0.3111 0 0 0 0 0 0.9234 0 0 0 0 0 0.4302 0 0 0 0 0 0.1848 0 0 0 0 0 0.9049 随机生成对角矩阵C>> C=diag([rand rand rand rand rand])C =0.9797 0 0 0 0 0 0.4389 0 0 0 0 0 0.1111 0 0 0 0 0 0.2581 0 0 0 0 0 0.4087 随机生成对角矩阵D>> D=diag([rand rand rand rand rand])D =0.5949 0 0 0 00 0.2622 0 0 00 0 0.6028 0 00 0 0 0.7112 00 0 0 0 0.2217>> Z=[A,B;C,D]Z =0.1948 0 0 0 00.3111 0 0 0 00 0.2259 0 0 00 0.9234 0 0 00 0 0.1707 0 00 0 0.4302 0 00 0 0 0.2277 0 0 0 0 0.1848 00 0 0 0 0.4357 0 0 0 0 0.90490.9797 0 0 0 00.5949 0 0 0 00 0.4389 0 0 00 0.2622 0 0 00 0 0.1111 0 00 0 0.6028 0 00 0 0 0.2581 00 0 0 0.7112 00 0 0 0 0.40870 0 0 0 0.2217计算Z的行列式>> det(Z)ans =-1.1243e-004计算det(A)*det(D)-det(B)*det(C)>> det(A)*det(D)-det(B)*det(C)ans =-9.3107e-005计算A*D-B*C的行列式>> det(A*D-B*C)ans =-1.1243e-004实验三求A列向量组的一个最大无关组，并把不属于极大无关组的向量利用极大无关组表示.N= 200865083;a=83;b=86;c=50;d=88;e=28;f=63;g=83;h=60;>>A=[a,b,c,d,3,4;1,2,3,4,4,3;12,15,22,17,5,7;e,f,g,h, 8,0];>> B=rref(A)B =1.0000 0 0 0 -0.3548 0.46560 1.0000 0 0 -1.4905 -2.00200 0 1.0000 0 0.0473 0.39500 0 0 1.0000 1.79841.3383所以a1,a2,a3,a4是一个极大无关组。