東華大學(xué)MATLAB數(shù)學(xué)實(shí)驗(yàn)第二版答案(胡良劍)

1、數(shù)學(xué)實(shí)驗(yàn)答案Chapter 1Page20,ex1(5) 等于 exp(1),exp(2);exp(3),exp(4)(7) 3=1*3, 8=2*4(8) a 為各列最小值， b 為最小值所在的行號(10) 1=4,false, 2=3,false, 3=2, ture, 4=1,ture(11) 答案表明：編址第 2 元素滿足不等式 (30=20) 和編址第 4 元素滿足不等式 (40=10)(12) 答案表明：編址第 2 行第 1 列元素滿足不等式 (30=20) 和編址第 2 行第 2 列元素滿足不等式 (40=10)Page20, ex2(1)a, b, c的值盡管都是1， 但數(shù)據(jù)類

2、型分別為數(shù)值，字符，邏輯，注意a 與c 相等，但他們不等于b(2)double(fun) 輸出的分別是字符a,b,s,(,x,)的ASCII碼Page20,ex3 r=2;p=0.5;n=12; T=log(r)/n/log(1+0.01*p)Page20,ex4 x=-2:0.05:2;f=x.4-2.x; fmin,min_index=min(f)最小值最小值點(diǎn)編址 x(min_index) ans =0.6500 最小值點(diǎn) f1,x1_index=min(abs(f)求近似根 -絕對值最小的點(diǎn)f1 =0.0328x1_index =24 x(x1_index) ans = -0.8500

3、 x(x1_index)=;f=x.4-2.x;刪去絕對值最小的點(diǎn)以求函數(shù)絕對值次小的點(diǎn) f2,x2_index=min(abs(f)求另一近似根 -函數(shù)絕對值次小的點(diǎn)f2 =0.0630x2_index =65 x(x2_index) ans =1.2500Page20,ex5 z=magic(10)z =92 99 1 8 15 67 74 51 58 4098 80 7 14 16 73 55 57 64 414 81 88 20 22 54 56 63 70 4785 87 19 21 3 60 62 69 71 2886 93 25 2 9 61 68 75 52 3417 24 7

4、6 83 90 42 49 26 33 6523 5 82 89 91 48 30 32 39 6679 6 13 95 97 29 31 38 45 7210 12 94 96 78 35 37 44 46 5311 18 100 77 84 36 43 50 27 59 sum(z) sum(diag(z) z(:,2)/sqrt(3) z(8,:)=z(8,:)+z(3,:)Chapter 2Page 45 ex1先在編輯器窗口寫下列M 函數(shù)，保存為eg2_1.mfunction xbar,s=ex2_1(x)n=length(x);xbar=sum(x)/n;s=sqrt(sum(x.

5、2)-n*xbar2)/(n-1);例如x=81 70 65 51 76 66 90 87 61 77;xbar,s=ex2_1(x)Page 45 ex2s=log(1);n=0;while sek=k+1;F(k)=F(k-1)+F(k-2); x=F(k)/F(k-1);enda,x,k計(jì)算至 k=21 可滿足精度Page 45 ex4clear;tic;s=0;for i=1:1000000s=s+sqrt(3)/2i;ends,toctic;s=0;i=1;while i1.1)+x.*(x=-1.1)-1.1*(x1);p=p+b*exp(-y.2-6*x.2).*(x+y-1).

6、*(x+y=1);p=p+a*exp(-0.75*y.2-3.75*x.2+1.5*x).*(x+y A=1 2 3;4 5 6;7 8 0;C=2 -5 -22;-5 -24 -56;-22 -56 -16; X=lyap(A,C)X =1.0000 -1.0000 -0.0000-1.0000 2.0000 1.0000-0.0000 1.0000 7.0000Chapter 3Page65 Ex1 a=1,2,3;b=2,4,3;a./b,a.b,a/b,ab ans =0.5000 0.5000 1.0000 ans =2 2 1 ans =0.6552 一元方程組 x2,4,3=1,

7、2,3 的近似解ans =0 0 00 0 00.6667 1.3333 1.0000矩陣方程 1,2,3x11,x12,x13;x21,x22,x23;x31,x32,x33=2,4,3的特解Page65 Ex 2(1) A=4 1 -1;3 2 -6;1 -5 3;b=9;-2;1; rank(A), rank(A,b)A,b 為增廣矩陣ans =3ans =3 可見方程組唯一解 x=Abx =2.38301.48942.0213(2) A=4 -3 3;3 2 -6;1 -5 3;b=-1;-2;1; rank(A), rank(A,b)ans =3ans =3 可見方程組唯一解 x=A

8、bx =-0.4706-0.29410(3) A=4 1;3 2;1 -5;b=1;1;1; rank(A), rank(A,b)ans =2ans =3 可見方程組無解 x=Abx =0.3311-0.1219最小二乘近似解(4) a=2,1,-1,1;1,2,1,-1;1,1,2,1;b=1 2 3;%注意 b 的寫法 rank(a),rank(a,b) ans =3ans =3rank(a)=rank(a,b) abans =1010 一個(gè)特解Page65 Ex3 a=2,1,-1,1;1,2,1,-1;1,1,2,1;b=1,2,3; x=null(a),x0=abx =-0.6255

9、0.6255-0.20850.4170x0 =1010通解 kx+x0Page65 Ex 4 x0=0.2 0.8;a=0.99 0.05;0.01 0.95; x1=a*x, x2=a2*x, x10=a10*x x=x0;for i=1:1000,x=a*x;end,xx =0.83330.1667 x0=0.8 0.2; x=x0;for i=1:1000,x=a*x;end,xx =0.83330.1667 v,e=eig(a)v =0.9806 -0.70710.1961 0.7071e =1.0000 00 0.9400 v(:,1)./x ans =1.17671.1767成比例

10、，說明x 是最大特征值對應(yīng)的特征向量Page65 Ex5用到公式 (3.11)(3.12) B=6,2,1;2.25,1,0.2;3,0.2,1.8;x=25 5 20; C=B/diag(x)0.2400 0.4000 0.05000.0900 0.2000 0.01000.1200 0.0400 0.0900 A=eye(3,3)-C A =0.7600 -0.4000 -0.0500 -0.0900 0.8000 -0.0100 -0.1200 -0.0400 0.9100 D=17 17 17;x=ADx =37.569625.786224.7690Page65 Ex 6(1) a=4

11、 1 -1;3 2 -6;1 -5 3;det(a),inv(a),v,d=eig(a) ans =-94 ans =0.2553 -0.0213 0.04260.1596 -0.1383 -0.22340.1809 -0.2234 -0.0532v =0.0185 -0.9009 -0.3066-0.7693 -0.1240 -0.7248-0.6386 -0.4158 0.6170d =-3.0527 0 00 3.6760 00 0 8.3766(2) a=1 1 -1;0 2 -1;-1 2 0;det(a),inv(a),v,d=eig(a) ans =1 ans =2.0000 -

12、2.0000 1.00001.0000 -1.0000 1.00002.0000 -3.0000 2.0000v =-0.5773 0.5774 + 0.0000i 0.5774 - 0.0000i-0.5773 0.5774 0.5774-0.5774 0.5773 - 0.0000i 0.5773 + 0.0000id =1.0000 0 00 1.0000 + 0.0000i 00 0 1.0000 - 0.0000i(3) A=5 7 6 5;7 10 8 7;6 8 10 9;5 7 9 10 A =5 7 6 57 10 8 76 8 10 95 7 9 10 det(A),inv

13、(A), v,d=eig(A)ans =1ans =68.0000 -41.0000 -17.0000 10.0000-41.0000 25.0000 10.0000 -6.0000-17.0000 10.0000 5.0000 -3.000010.0000 -6.0000 -3.0000 2.0000v =0.8304 0.0933 0.3963 0.3803-0.5016 -0.3017 0.6149 0.5286-0.2086 0.7603 -0.2716 0.55200.1237 -0.5676 -0.6254 0.5209d =0.0102 0 0 00 0.8431 0 00 0

14、3.8581 00 0 0 30.2887(4) (以 n=5 為例 )方法一（三個(gè)for ）n=5;for i=1:n, a(i,i)=5;endfor i=1:(n-1),a(i,i+1)=6;endfor i=1:(n-1),a(i+1,i)=1;enda方法二（一個(gè)for ）n=5;a=zeros(n,n);a(1,1:2)=5 6;for i=2:(n-1),a(i,i-1,i,i+1)=1 5 6;enda(n,n-1 n)=1 5;a方法三（不用for ）n=5;a=diag(5*ones(n,1);b=diag(6*ones(n-1,1);c=diag(ones(n-1,1);

15、a=a+zeros(n-1,1),b;zeros(1,n)+zeros(1,n);c,zeros(n-1,1)下列計(jì)算 det(a) ans = 665 inv(a) ans =0.3173 -0.5865 1.0286 -1.6241 1.9489 -0.0977 0.4887 -0.8571 1.3534 -1.6241 0.0286 -0.1429 0.5429 -0.8571 1.0286-0.0075 0.0376 -0.1429 0.4887 -0.58650.0015 -0.0075 0.0286 -0.0977 0.3173 v,d=eig(a)v =-0.7843 -0.78

16、43 -0.9237 0.9860 -0.9237 0.5546 -0.5546 -0.3771 -0.0000 0.3771 -0.2614 -0.2614 0.0000 -0.1643 0.0000 0.0924 -0.0924 0.0628 -0.0000 -0.0628 -0.0218 -0.0218 0.0257 0.0274 0.0257 d =0.7574 0 0 0 00 9.2426 0 0 00 0 7.4495 0 00 0 0 5.0000 00 0 0 0 2.5505Page65 Ex 7(1) a=4 1 -1;3 2 -6;1 -5 3;v,d=eig(a)v

17、=0.0185 -0.9009 -0.3066 -0.7693 -0.1240 -0.7248 -0.6386 -0.4158 0.6170 d =-3.0527 0 0 0 3.6760 0 0 0 8.3766 det(v)ans =-0.9255 %v 行列式正常 , 特征向量線性相關(guān)，可對角化 inv(v)*a*v驗(yàn)算ans =-3.0527 0.0000 -0.00000.00003.6760-0.0000-0.0000 -0.0000 8.3766 v2,d2=jordan(a)也可用 jordanv2 =0.07980.00760.91270.1886-0.3141 0.1256

18、-0.1605 -0.2607 0.4213特征向量不同d2 =8.3766 0 00 -3.0527 - 0.0000i 00 0 3.6760 + 0.0000i v2a*v2ans =8.3766 0 0.00000.0000 -3.0527 0.00000.0000 0.0000 3.6760 v(:,1)./v2(:,2)對應(yīng)相同特征值的特征向量成比例ans =2.44912.44912.4491(2) a=1 1 -1;0 2 -1;-1 2 0;v,d=eig(a)v =-0.5773 0.5774 + 0.0000i 0.5774 - 0.0000i -0.5773 0.577

19、4 0.5774-0.5774 0.5773 - 0.0000i 0.5773 + 0.0000i d =1.0000 0 00 1.0000 + 0.0000i 00 0 1.0000 - 0.0000i det(v)ans =-5.0566e-028 -5.1918e-017iv 的行列式接近0, 特征向量線性相關(guān)，不可對角化 v,d=jordan(a)v =1 0 11 0 01 -1 0d =1 1 00 1 10 0 1jordan 標(biāo)準(zhǔn)形不是對角的，所以不可對角化(3) A=5 7 6 5;7 10 8 7;6 8 10 9;5 7 9 10 A =5 7 6 57 10 8 76

20、 8 10 95 7 9 10 v,d=eig(A)v =0.8304 0.0933 0.3963 0.3803 -0.5016 -0.3017 0.6149 0.5286 -0.2086 0.7603 -0.2716 0.5520 0.1237 -0.5676 -0.6254 0.5209d =0.0102 0 0 00 0.8431 0 00 0 3.8581 00 0 0 30.2887 inv(v)*A*v ans =0.0102 0.0000 -0.0000 0.00000.0000 0.8431 -0.0000 -0.0000 -0.0000 0.0000 3.8581 -0.00

21、00-0.0000 -0.0000 0 30.2887本題用 jordan 不行 , 原因未知(4)參考 6(4)和 7(1)Page65 Exercise 8只有 (3) 對稱 , 且特征值全部大于零, 所以是正定矩陣.Page65 Exercise 9(1) a=4 -3 1 3;2 -1 3 5;1 -1 -1 -1;3 -2 3 4;7 -6 -7 0 rank(a)ans =3 rank(a(1:3,:) ans =2 rank(a(1 2 4,:)1,2,4 行為最大無關(guān)組ans =3 b=a(1 2 4,:);c=a(3 5,:); bc線性表示的系數(shù)ans =0.5000 5.

22、0000-0.5000 1.00000 -5.0000Page65 Exercise 10 a=1 -2 2;-2 -2 4;2 4 -2 v,d=eig(a)v =0.3333 0.9339 -0.12930.6667 -0.3304 -0.6681-0.6667 0.1365 -0.7327d =-7.0000 0 00 2.0000 00 0 2.0000 v*vans =1.0000 0.0000 0.00000.0000 1.0000 00.0000 0 1.0000v 確實(shí)是正交矩陣Page65 Exercise 11設(shè)經(jīng)過 6 個(gè)電阻的電流分別為i1, ., i6. 列方程組如下

23、20-2i1=a; 5-3i2=c; a-3i3=c; a-4i4=b; c-5i5=b; b-3i6=0;i1=i3+i4;i5=i2+i3;i6=i4+i5;計(jì)算如下 A=1 0 0 2 0 0 0 0 0;0 0 1 0 3 0 0 0 0;1 0 -1 0 0 -3 0 0 0; 1 -1 0 0 0 0 -4 0 0; 0 -1 1 0 0 0 0 -5 0;0 1 0 0 0 0 0 0 -3; 0 0 0 1 0 -1 -1 0 0;0 0 0 0 -1 -1 0 1 0; 0 0 0 0 0 0 -1 -1 1;b=20 5 0 0 0 0 0 0 0; Ab ans =13.

24、34536.44018.54203.3274 -1.1807 1.60111.72630.42042.1467Page65 Exercise 12 A=1 2 3;4 5 6;7 8 0; left=sum(eig(A), right=sum(trace(A) left =6.0000 right =6 left=prod(eig(A), right=det(A) 原題有錯(cuò) , (-1)n 應(yīng)刪去 left =27.0000right =27 fA=(A-p(1)*eye(3,3)*(A-p(2)*eye(3,3)*(A-p(3)*eye(3,3) fA =1.0e-012 *0.0853 0

25、.1421 0.02840.1421 0.1421 0-0.0568 -0.1137 0.1705 norm(fA)f(A) 范數(shù)接近 0ans =2.9536e-013Chapter 4Page84 Exercise 1(1)roots(1 1 1)(2)roots(3 0 -4 0 2 -1)(3)p=zeros(1,24);p(1 17 18 22)=5 -6 8 -5;roots(p)(4)p1=2 3;p2=conv(p1, p1);p3=conv(p1, p2);p3(end)=p3(end)-4; % 原 p3 最后一個(gè)分量-4roots(p3)Page84Exercise 2f

26、un=inline(x*log(sqrt(x2-1)+x)-sqrt(x2-1)-0.5*x);fzero(fun,2)Page84Exercise 3fun=inline(x4-2x);fplot(fun,-2 2);grid on;fzero(fun,-1),fzero(fun,1),fminbnd(fun,0.5,1.5)Page84Exercise 4fun=inline(x*sin(1/x),x);fplot(fun, -0.1 0.1);x=zeros(1,10);for i=1:10, x(i)=fzero(fun,(i-0.5)*0.01);end;x=x,-xPage84Ex

27、ercise 5fun=inline(9*x(1)2+36*x(2)2+4*x(3)2-36;x(1)2-2*x(2)2-20*x(3);16*x(1)-x(1)3-2*x(2) 2-16*x(3)2,x);a,b,c=fsolve(fun,0 0 0)Page84Exercise 6fun=(x)x(1)-0.7*sin(x(1)-0.2*cos(x(2),x(2)-0.7*cos(x(1)+0.2*sin(x(2); a,b,c=fsolve(fun,0.5 0.5)Page84Exercise 7clear; close; t=0:pi/100:2*pi;x1=2+sqrt(5)*cos

28、(t); y1=3-2*x1+sqrt(5)*sin(t);x2=3+sqrt(2)*cos(t); y2=6*sin(t);plot(x1,y1,x2,y2); grid on; 作圖發(fā)現(xiàn) 4 個(gè)解的大致位置，然后分別求解 y1=fsolve(x(1)-2)2+(x(2)-3+2*x(1)2-5,2*(x(1)-3)2+(x(2)/3)2-4,1.5,2) y2=fsolve(x(1)-2)2+(x(2)-3+2*x(1)2-5,2*(x(1)-3)2+(x(2)/3)2-4,1.8,-2) y3=fsolve(x(1)-2)2+(x(2)-3+2*x(1)2-5,2*(x(1)-3)2+(

29、x(2)/3)2-4,3.5,-5) y4=fsolve(x(1)-2)2+(x(2)-3+2*x(1)2-5,2*(x(1)-3)2+(x(2)/3)2-4,4,-4)Page84Exercise 8(1)clear;fun=inline(x.2.*sin(x.2-x-2);fplot(fun,-2 2);grid on;作圖觀察x(1)=-2;x(3)=fminbnd(fun,-1,-0.5);x(5)=fminbnd(fun,1,2);fun2=inline(-x.2.*sin(x.2-x-2);x(2)=fminbnd(fun2,-2,-1);x(4)=fminbnd(fun2,-0.

30、5,0.5);x(6)=2feval(fun,x)答案 :以上x(1)(3)(5)是局部極小， x(2)(4)(6)是局部極大，從最后一句知道x(1) 全局最小，x(2)最大。(2)clear;fun=inline(3*x.5-20*x.3+10);fplot(fun,-3 3);grid on;作圖觀察x(1)=-3;x(3)=fminsearch(fun,2.5);fun2=inline(-(3*x.5-20*x.3+10);x(2)=fminsearch(fun2,-2.5);x(4)=3;feval(fun,x)(3)fun=inline(abs(x3-x2-x-2);fplot(fu

31、n,0 3);grid on;作圖觀察fminbnd(fun,1.5,2.5)fun2=inline(-abs(x3-x2-x-2);fminbnd(fun2,0.5,1.5)Page84 Exercise 9close;x=-2:0.1:1;y=-7:0.1:1;x,y=meshgrid(x,y);z=y.3/9+3*x.2.*y+9*x.2+y.2+x.*y+9;mesh(x,y,z);grid on;作圖觀察fun=inline(x(2)3/9+3*x(1)2*x(2)+9*x(1)2+x(2)2+x(1)*x(2)+9);x=fminsearch(fun,0 0)求極小值fun2=in

32、line(-(x(2)3/9+3*x(1)2*x(2)+9*x(1)2+x(2)2+x(1)*x(2)+9);x=fminsearch(fun2,0 -5)求極大值Page84Exercise 10clear;t=0:24;c=15 14 14 14 14 15 16 18 20 22 23 25 28 .31 32 31 29 27 25 24 22 20 18 17 16;p2=polyfit(t,c,2)p3=polyfit(t,c,3)fun=inline(a(1)*exp(a(2)*(t-14).2),a,t);a=lsqcurvefit(fun,0 0,t,c)初值可以試探f=fe

33、val(fun, a,t)norm(f-c)擬合效果plot(t,c,t,f)作圖檢驗(yàn)fun2=inline(b(1)*sin(pi/12*t+b(2)+20,b,t);原題修改 f(x)+20b=lsqcurvefit(fun2,0 0,t,c)figuref2=feval(fun2, b,t)norm(f2-c)擬合效果plot(t,c,t,f2)作圖檢驗(yàn)Page84Exercise 11fun=inline(1-x)*sqrt(10.52+x)-3.06*x*sqrt(1+x)*sqrt(5);x=fzero(fun, 0, 1)Page84 Exercise 12r=5.04/12/1

34、00;N=20*12;x=7500*180房屋總價(jià)格y=x*0.3首付款額x0=x-y貸款總額a=(1+r)N*r*x0/(1+r)N-1)月付還款額r1=4.05/12/100;x1=10*10000;公積金貸款a1=(1+r1)N*r1*x1/(1+r1)N-1)x2=x0-x1商業(yè)貸款a2=(1+r)N*r*x2/(1+r)N-1)a=a1+a2Page84 Exercise 13列方程 th*R2+(pi-2*th)*r2-R*r*sin(th)=pi*r2/2化簡得 sin(2*th)-2*th*cos(2*th)=pi/2以下 Matlab 計(jì)算clear;fun= inline(

35、sin(2*th)-2*th*cos(2*th)-pi/2,th)th=fsolve(fun,pi/4)R=20*cos(th)Page84 Exercise 14先在 Editor 窗口寫 M 函數(shù)保存function x=secant(fname,x0,x1,e)while abs(x0-x1)e,x=x1-(x1-x0)*feval(fname,x1)/(feval(fname,x1)-feval(fname,x0);x0=x1;x1=x;end再在指令窗口fun=inline(x*log(sqrt(x2-1)+x)-sqrt(x2-1)-0.5*x);secant(fun,1,2,1e

36、-8)Page84 Exercise 15作系數(shù)為a,初值為 xo,從第 m 步到第 n 步迭代過程的M 函數(shù)：function f=ex4_15fun(a,x0,m,n)x(1)=x0; y(1)=a*x(1)+1;x(2)=y(1);if mm, plot(x(i),x(i),x(i+1),y(i-1),y(i),y(i); endendhold off;M 腳本文件subplot(2,2,1);ex4_15fun(0.9,1,1,20);subplot(2,2,2);ex4_15fun(-0.9,1,1,20);subplot(2,2,3);ex4_15fun(1.1,1,1,20);s

37、ubplot(2,2,4);ex4_15fun(-1.1,1,1,20);Page84 Exercise 16設(shè)夾角 t, 問題轉(zhuǎn)化為min f=5/sin(t)+10/cos(t)取初始值pi/4, 計(jì)算如下fun=(t)5/sin(t)+10/cos(t);t,f=fminsearch(fun, pi/4)t =0.6709f =20.8097Page84 Exercise 17提示： x(k+2)=f(x(k)=a2*x(k)*(1-x(k)*(1-a*x(k)*(1-x(k)計(jì)算平衡點(diǎn)x|f(x)| ex4_18(0.9,1,20) ex4_18(-0.9,1,20) ex4_18(1

38、.1,1,20) ex4_18(-1.1,1,20)Page84 Exercise 19clear; close; x(1)=0; y(1)=0;for k=1:3000x(k+1)=1+y(k)-1.4*x(k)2; y(k+1)=0.3*x(k);endplot(x(1000:1500),y(1000:1500),+g);hold onplot(x(1501:2000),y(1501:2000),.b);plot(x(2001:2500),y(2001:2500),*y);plot(x(2501:3001),y(2501:3001),.r);Chapter 5Page101 Exercis

39、e 1x=0 4 10 12 15 22 28 34 40;y=0 1 3 6 8 9 5 3 0;trapz(x,y)Page101 Exercise 2x=0 4 10 12 15 22 28 34 40;y=0 1 3 6 8 9 5 3 0;diff(y)./diff(x)Page101 Exercise 3xa=-1:0.1:1;ya=0:0.1:2;x,y=meshgrid(xa,ya);z=x.*exp(-x.2 -y.3);px,py = gradient(z,xa,ya);pxPage101 Exercise 4t=0:0.01:1.5;x=log(cos(t);y=cos(

40、t)-t.*sin(t);dydx=gradient(y,x)x_1,id=min(abs(x-(-1);%找最接近x=-1 的點(diǎn)dydx(id)Page101 Exercise 5(1)Fun=inline( 1/(sqrt(2*pi).*exp(-x.2./2);Quadl(fun,0,1)(2)fun=inline(exp(2*x).*cos(x).3);quadl(fun,0,2*pi)或用 trapzx=linspace(0,2*pi,100);y=exp(2*x).*cos(x).3;trapz(x,y)(3)fun=(x)x.*log(x.4).*asin(1./x.2);qua

41、dl(fun,1,3)或用 trapzx=1:0.01:3;y=feval(fun,x);trapz(x,y)(4)fun=(x)sin(x)./x;quadl(fun,1e-10,1) % 注意由于下限為0，被積函數(shù)沒有意義，用很小的1e-10 代替(5)%參考 Exercise 5(4)(6)fun=inline(sqrt(1+r.2.*sin(th),r,th);dblquad(fun,0,1,0,2*pi)(7)首先建立84 頁函數(shù) dblquad2clear;fun=(x,y)1+x+y.2;clo=(x)-sqrt(2*x-x.2);dup=(x)sqrt(2*x-x.2);dbl

42、quad2(fun,0,2,clo,dhi,100)Page101Exercise 6t=linspace(0,2*pi,100);x=2*cos(t);y=3*sin(t);dx=gradient(x,t);dy=gradient(y,t);f=sqrt(dx.2+dy.2);trapz(t,f)Page101 Exercise 7xa=-1:0.1:1;ya=0:0.1:2;x,y=meshgrid(xa,ya);z=x.*exp(x.2+y.2);zx,zy=gradient(z,xa,ya);f=sqrt(1+zx.2+zy.2);s=0;for i=2:length(xa)for j=2:length(ya)s=s+(xa(i)-x