matlab实验练习题(计算机)-南邮-matlab-数学实验大作业答案

1“MATLAB”练习题练习题要求：抄题、写出操作命令、运行结果，并根据要求，贴上运行图。1、求的所有根。 (先画图后求解) (要求贴图)230xex solve(exp(x)-3*x2,0)ans =-2*lambertw(-1/6*3(1/2)-2*lambertw(-1,-1/6*3(1/2)-2*lambertw(1/6*3(1/2)2、求下列方程的根。1) 5510xx a=solve(x5+5*x+1,0);a=vpa(a,6)2a =1.10447+1.05983*i-1.00450+1.06095*i-.199936-1.00450-1.06095*i1.10447-1.05983*i2)至 少三个根 1sin02xx fzero(x*sin(x)-1/2, 3)ans =2.9726 fzero(x*sin(x)-1/2,-3)ans =-2.9726 fzero(x*sin(x)-1/2,0)ans =-0.740833) 所有根2sin cos0xxx fzero(sin(x)*cos(x)-x2,0)ans =0 fzero(sin(x)*cos(x)-x2,0.6)ans =0.70223、求解下列各题：1) 30sinlim xxx x sym x; limit(x-sin(x)/x3)ans =1/62) (10)cos ,xyexy求 sym x; diff(exp(x)*cos(x),10)ans =4(-32)*exp(x)*sin(x)3) 21/20(17xe dx精确到位有效数字) sym x; vpa(int(exp(x2),x,0,1/2),17)ans =0.544987104183622224)42254xdxx sym x; int(x4/(25+x2),x)ans =125*atan(x/5) - 25*x + x3/35)求由参数方程所确定的函数的一阶导数与二阶导数。2ln 1 arctanxt yt dy dx22d y dx sym t; x=log(sqrt(1+t2);y=atan(t); diff(y,t)/diff(x,t)ans =1/t6)设函数 y=f(x)由方程 xy +ey= e 所确定，求 y(x)。 syms x y; f=x*y+exp(y)-exp(1); -diff(f,x)/diff(f,y)ans =-y/(x + exp(y)57) 0sin2xexdx syms x; y=exp(-x)*sin(2*x); int(y,0,inf)ans =2/58) 108xx将在展开(最高次幂为) syms x f=sqrt(1+x); taylor(f,0,9)ans =- (429*x8)/32768 + (33*x7)/2048 - (21*x6)/1024 + (7*x5)/256 - (5*x4)/128 + x3/16 - x2/8 + x/2 + 19) 1sin(3)(2)xyey求 syms x y; y=exp(sin(1/x); dy=subs(diff(y,3),x,2)dy =-0.582610)求变上限函数对变量 x 的导数。2xxatdt syms a t;6 diff(int(sqrt(a+t),t,x,x2) Warning: Explicit integral could not be found. ans =2*x*(x2 + a)(1/2) - (a + x)(1/2)4、求点(1,1,4)到直线 L: 的距离 31 102xyz M0=1,1,4;M1=3,0,1;M0M1=M1-M0; v=-1,0,2; d=norm(cross(M0M1,v)/norm(v)d =1.09545、已知分别在下列条件下画出的图形：(要求贴图)22()21( ),2x f xe ( )f x，在同一坐标系里作图(1)1,01 1 时， syms x; fplot(1/sqrt(2*pi)*exp(-(x)2)/2),-3,3,r) hold on fplot(1/sqrt(2*pi)*exp(-(x-1)2)/2),-3,3,y) hold on fplot(1/sqrt(2*pi)*exp(-(x+1)2)/2),-3,3,g) hold off，在同一坐标系里作图。(2)0,1 2 4时，7 syms x; fplot(1/sqrt(2*pi)*exp(-(x)2)/2),-3,3,r) hold on fplot(1/(sqrt(2*pi)*2)*exp(-(x)2)/(2*22),-3,3,y) hold on fplot(1/(sqrt(2*pi)*4)*exp(-(x)2)/(2*42),-3,3,g) hold off6、画下列函数的图形：(要求贴图)(1) sin020cos024xuttyututz ezmesh(u*sin(t),u*cos(t),t/4,0,20,0,2)(2) sin()03,03zxyxy x=0:0.1:3;y=x; X Y=meshgrid(x,y); Z=sin(X*Y); mesh(X,Y,Z)8(3) sin (3cos )02cos (3cos )02sinxtutytuuzu ezmesh(sin(t)*(3+cos(u),cos(t)*(3+cos(u),sin(u),0,2*pi,0,2*pi)7、 已知，在 MATLAB 命令窗口中建立 A、B 矩阵422134 305 ,203 153211AB 并对其进行以下操作：(1) 计算矩阵 A 的行列式的值det( )A A=4,-2,2;-3,0,5;1,5,3; det(A)ans =-158(2) 分别计算下列各式：1122,* , .* ,TAB A B AB ABA B AA9 A=4,-2,2;-3,0,5;1,5,3;B=1,3,4;-2,0,-3;2,-1,1; 2*A-Bans =7 -7 0-4 0 130 11 5 A*Bans =12 10 247 -14 -7-3 0 -8 A.*Bans =4 -6 86 0 -152 -5 3 A*inv(B)ans =-0.0000 -0.0000 2.0000-2.7143 -8.0000 -8.14292.4286 3.0000 2.2857 inv(A)*Bans =0.4873 0.4114 1.00000.3671 -0.4304 0.0000-0.1076 0.2468 0.0000 A*A10ans =24 2 4-7 31 9-8 13 36 Aans =4 -3 1-2 0 52 5 38、 在 MATLAB 中分别利用矩阵的初等变换及函数 rank、函数 inv 求下列矩阵的秩：(1) 求 rank(A)=? 1632 3540 , 11124A A=1,-6,3,2;3,-5,4,0;-1,-11,2,4; rank(A)ans =3(2) 求。3501 1200,1020 1202B 1B B=3,5,0,1;1,2,0,0;1,0,2,0;1,2,0,2 inv(B)ans =2.0000 -4.0000 -0.0000 -1.0000-1.0000 2.5000 0.0000 0.5000-1.0000 2.0000 0.5000 0.50000 -0.5000 0 0.50009、在 MATLAB 中判断下列向量组是否线性相关，并找出向量组1(1132) ,T11中的一个最大线性无关组。234( 11 13) ,(5289) ,( 1317)TTT a1=1 1 3 2 a2=-1 1 -1 3 a3=5 -2 8 9 a4=-1 3 1 7 A= a1, a2 ,a3 ,a4 ;R jb=rref(A)a1 =1132a2 =-11-13a3 =5-289a4 =-1317R =1.0000 0 0 1.0909120 1.0000 0 1.78790 0 1.0000 -0.06060 0 0 0jb =1 2 3 A(:,jb)ans =1 -1 51 1 -23 -1 82 3 9 10、在 MATLAB 中判断下列方程组解的情况，若有多个解，写出通解。(1) 1234123412341234420 20 3720 31260xxxx xxxx xxxx xxxx 一： A=1,-1,4,2;1,-1,-1,2;3,1,7,-2;1,-3,-12,6; rank(A)ans =3 rref(A)ans =1 0 0 00 1 0 -20 0 1 00 0 0 0 二： A=1,-1,4,2;1,-1,-1,2;3,1,7,-2;1,-3,-12,6; format rat n=4; RA=rank(A)13RA =3 if(RA=n)fprintf(%方程只有零解) elseb=null(A,r) endb =0 2 0 1 syms k X=k*bX =02*k0k(2) 123123123123234 245 38213 496xxx xxx xxx xxx A=2 3 1;1 -2 4;3 8 -2;4 -1 9; b=4 -5 13 -6; B=A b; n=3; RA=rank(A)RA =2 RB=rank(B)RB =142 rref(B)ans =1 0 2 -1 0 1 -1 2 0