>> d=deconv([3 13 6 8],[1 4]) d =
3 1 2
12. 对下式进行部分分式展开：(提示：用函数)
3x4?2x3?5x2?4x?6x5?3x4?4x3?2x2?7x?2
>> a=[1 3 4 2 7 2]; >> b=[3 2 5 4 6];
>> [r,s,k]=residue(b,a) r =
1.1274 + 1.1513i 1.1274 - 1.1513i -0.0232 - 0.0722i -0.0232 + 0.0722i 0.7916 s =
-1.7680 + 1.2673i -1.7680 - 1.2673i 0.4176 + 1.1130i 0.4176 - 1.1130i -0.2991 k = []
13. 计算多项式4x4?12x3?14x2?5x?9的微分和积分。(提示：用函数)
>> p=[4 –12 –14 5]; >> pder=polyder(p);
>> pders=poly2sym(pder) >> pint=polyint(p);
>> pints=poly2sym(pint) pders =
12*x^2-24*x-14 pints =
x^4-4*x^3-7*x^2+5*x
?290??13????14. 解方程组??3411?x??6?。
???226???6??
15. 求欠定方程组??2474??8?x???5?的最小范数解。(提示：用函数)
?9356???
>> a=[2 4 7 4;9 3 5 6]; >> b=[8 5]'; >> x=pinv(a)*b x =
-0.2151 0.4459 0.7949 0.2707
?42?6??16. 矩阵a???754?，计算a的行列式和逆矩阵。(提示：用函数)
??349??
>> a=[4 2 -6;7 5 4 ;3 4 9]; >> ad=det(a) >> ai=inv(a) ad = -64 ai =
-0.4531 0.6562 -0.5937 0.7969 -0.8437 0.9062 -0.2031 0.1562 -0.0937
17. x??12345?，y??246810?，计算x的协方差、y的协方差、x与y的互协方差。(提示：用函数)
>> x=[1 2 3 4 5]; >> y=[2 4 6 8 10]; >> cx=cov(x) >> cy=cov(y) >> cxy=cov(x,y) cx =
2.5000 cy = 10 cxy =
2.5000 5.0000 5.0000 10.0000
18. 参照例3-20的方法，计算表达式z?10x3?y5e?x??2?y2的梯度并绘图。(提示：用函数)
>> v = -2:0.2:2;
>> [x,y] = meshgrid(v);
>> z=10*(x.^3-y.^5).*exp(-x.^2-y.^2); >> [px,py] = gradient(z,.2,.2); >> contour(x,y,z) >> hold on
>> quiver(x,y,px,py) >> hold off
19. 有一正弦衰减数据y=sin(x).*exp(-x/10)，其中x=0:pi/5:4*pi，用三次样条法进行插值。(提示：用函数)
>> x0=0:pi/5:4*pi;
>> y0=sin(x0).*exp(-x0/10); >> x=0:pi/20:4*pi; >> y=spline(x0,y0,x); >> plot(x0,y0,'or',x,y,'b')
20. 求矩阵A???a11?a21a12?的行列式值、逆和特征根。(提示：用函数) a22??
>> syms a11 a12 a21 a22; >> A=[a11,a12;a21,a22]
>> AD=det(A) % 行列式 >> AI=inv(A) % 逆
>> AE=eig(A) % 特征值 A =
[ a11, a12] [ a21, a22] AD =
a11*a22-a12*a21 AI =
[ -a22/(-a11*a22+a12*a21), a12/(-a11*a22+a12*a21)] [ a21/(-a11*a22+a12*a21), -a11/(-a11*a22+a12*a21)] AE =
[ 1/2*a11+1/2*a22+1/2*(a11^2-2*a11*a22+a22^2+4*a12*a21)^(1/2)] [ 1/2*a11+1/2*a22-1/2*(a11^2-2*a11*a22+a22^2+4*a12*a21)^(1/2)]
21. 因式分解：x4?5x3?5x2?5x?6(提示：用函数)
>> syms x;
>> f=x^4-5*x^3+5*x^2+5*x-6; >> factor(f) ans =
(x-1)*(x-2)*(x-3)*(x+1)
?a22. f???ax?e1?x?，用符号微分求df/dx。(提示：用函数) ?log(x)sin(x)?x2
>> syms a x;
>> f=[a, x^2, 1/x; exp(a*x), log(x), sin(x)]; >> df=diff(f) df =
[ 0, 2*x, -1/x^2] [ a*exp(a*x), 1/x, cos(x)]
??ax2?by?c?023. 求代数方程组?关于x,y的解。(提示：用函数)
?x?y?0?
>> S=solve('a*x^2+b*y+c=0','b*x+c=0','x','y'); >> disp('S.x=') , disp(S.x) >> disp('S.y=') , disp(S.y) S.x=
-c/b S.y=
-c*(a*c+b^2)/b^3
24. 符号函数绘图法绘制函数x=sin(3t)cos(t)，y=sin(3t)sin(t)的图形，t的变化范围为[0,2?]。(提示：用函数)
>> syms t
>> ezplot(sin(3*t)*cos(t),sin(3*t)*sin(t),[0,pi])
25. 绘制极坐标下sin(3*t)*cos(t)的图形。(提示：用函数)
>> syms t
>> ezpolar(sin(3*t)*cos(t)
26. 绘制曲线y?x3?x?1，x的取值范围为[-5,5]。(提示：用函数)
>> x=-5:0.2:5; >> y=x.^3+x+1; >> plot(x,y)