MATLAB练习题.doc

习题3 【p81】1.用M文件建立:%第一题F001%定义函数（下述代码另存为工作目录下的f001.m文件）X=1.23 2.34 3.45 4.56 5.67 6.78 2.13 3.24 4.35 5.46 6.57 7.68 3.42 4.53 5.64 6.75 7.86 8.97运行结果如下：用文本文件建立:%第二题load f002.txtf002%定义f002.txt函数（下述代码另存为工作目录下的f002.txt文件） 1.23 2.34 3.45 4.56 5.67 6.78 2.13 3.24 4.35 5.46 6.57 7.68 3.42 4.53 5.64 6.75 7.86 8.97运行结果：5.1.特征值对角阵：V,D=eig(A)运行结果：V = -4216/5113 -250/601 671/1186 -1736/1909 D = -736/1977 0 0 1977/368 2.特征值：d=eig(A)运行结果：d = -736/1977 1977/368 3.逆：A=1 2;3 4;format ratB=inv(A)运行结果：B = -2 1 3/2 -1/2 4.转置：B=A运行结果：B = 1 3 2 4 5.条件数：c=cond(A)运行结果：c = 14.93306.求秩:A=1 2;3 4;r=rank(A)运行结果：r = 26.Cholesky分解：R,p=chol(A)运行结果：R = 1 p = 2 LU分解：L,U=lu(A)运行结果：L = 1/3 1 1 0 U = 3 4 0 2/3 QR分解：Q,R=qr(A)运行结果：Q = -0.3162 -0.9487 -0.9487 0.3162R = -3.1623 -4.4272 0 -0.6325Schur分解：U,T=schur(A)运行结果：U = -0.8246 -0.5658 0.5658 -0.8246T = -0.3723 -1.0000 0 5.37237（1）(矩阵除法解法)代码：A=1 -2 3 -4;-2 3 -4 5;-3 4 5 -6;4 -5 -6 7;b=1 2 3 4;R_A=rank(A)X=Ab运行结果：R_A = 4X = 12.0000 10.0000 -29.0000 -24.0000（2）（函数rref求解）代码： A=1 1 3 -1 -2;0 1 -1 1 1;1 1 2 2 4;1 -1 1 -1 0; R=rref(A)运行结果：R = 1 0 0 0 1 0 1 0 0 -1 0 0 1 0 0 0 0 0 1 2则R的最后一行元素就是所求之解。习题4【P89】2.代码：x=0.0 0.5 1.0 1.5;y=0.0 0.5 1.0 1.5;z=50 49 50 49;49 49 49 49;49 48 48 47;48 48 47 46;x1=1.2;y1=1.4;z11=interp2(x,y,z,x1,y1,bicubic)结果：z11 = 46.8112z11=interp2(x,y,z,x1,y1,bilinear)结果：z11 = 46.8000z11=interp2(x,y,z,x1,y1,nearest)结果：z11 = 473.最大值：maxy=max(y)结果：maxy = 8最小值：miny=min(y)结果：miny = 2均值：meany=mean(y)结果：meany = 4.7500中值: mediany=median(y)结果：mediany = 4.5000标准差：stdy=std(y)结果：stdy = 2.7538习题5【P107】1. 代码：xx,fx,out=fzero(sin(x)+cos(x),0.0)运行结果：xx = -0.7854fx = -1.1102e-16out = 14.极值：代码：f=inline(sin(x)/x);x1=fminbnd(f,0,2)结果：x1 = 2.0000零点：xx,fx,out=fzero(sin(x)/x,1.0)结果：xx = 3.1416fx = 1.8034e-16out = 15.%在区间0 20 求函数在y(1)=2,y(2)=0时的积分结果x,y=ode45(f0506,0 20,2;0);plot(x,y);%定义f0506函数（下述代码另存为工作目录下的f0506.m文件 ）function y=f0506(x,y);y=y(2);y(2)-y(1);习题6 p【123】1.代码： clear syms k x y a b; r1=symsum(x(2*k)/sym(k!),k,0,inf) 运行结果：r1 = exp(x2)2.（4）代码：clear syms x a; r11=a*(1+1/x)x; r12=limit(r11,x,inf,left) 运行结果：r12 = a*exp(1)6.（2）代码： syms x z; r1=int(x*sin(x),0,1) 运行结果：r1 = sin(1) - cos(1) 11计算矩阵A=a b;c d的逆。代码： syms a b c d; A=a b;c d; B=inv(A) 运行结果：B = d/(a*d - b*c), -b/(a*d - b*c) -c/(a*d - b*c), a/(a*d - b*c)习题7 p150代码：clear x=(0:0.01:2)*pi; y1=cos(x); y2=cos(2*x); y3=cos(3*x); y4=cos(4*x); a=subplot(2,2,1);plot(x,y1) a=subplot(2,2,2);plot(x,y2) a=subplot(2,2,3);plot(x,y3) a=subplot(2,2,4);plot(x,y4)截图：4.代码：clf x=(4:0.01:10); y1=sin(x); y2=cos(x); y3=x.2; y4=x; plot(x,y1,r-); plot(x,y2,b-); hold on; plot(x,y1,r-); hold on