matlab实验习题4---5

matlab实验习题

实验四

1、求A逆矩阵

1、求A行列式

det(A)

ans =

-64

2、求A迹

trace(A)

ans =

18

3、求A秩

rank(A)

ans =

3

4、求A的SVD分解，产生与A维数相同的、非负的对角线元素以降幂排列的对角矩阵S和单元矩阵U、V，使得A=U*S*V’

s=svd(A)

matlab实验习题

s =

13.3272

8.6066

0.5580

>> [U,S,V]=svd(A)

U =

0.1372 0.8425 0.5210

-0.6414 0.4764 -0.6014

-0.7548 -0.2517 0.6057 S =

13.3272 0 0

0 8.6066 0

0 0 0.5580 V =

-0.4656 0.6912 -0.5526

-0.4466 0.3555 0.8211

-0.7640 -0.6291 -0.1432 >> [U,S,V]=svd(A,0)

U =

0.1372 0.8425 0.5210

-0.6414 0.4764 -0.6014

-0.7548 -0.2517 0.6057 S =

13.3272 0 0

0 8.6066 0

0 0 0.5580

matlab实验习题

V =

-0.4656 0.6912 -0.5526

-0.4466 0.3555 0.8211

-0.7640 -0.6291 -0.1432

>> [U,S,V]=svd(A,'econ')

U =

0.1372 0.8425 0.5210

-0.6414 0.4764 -0.6014

-0.7548 -0.2517 0.6057

S =

13.3272 0 0

0 8.6066 0

0 0 0.5580

V =

-0.4656 0.6912 -0.5526

-0.4466 0.3555 0.8211

-0.7640 -0.6291 -0.1432

5、求A的特征值和特征向量，返回矩阵A的特征值矩阵D和特征向量矩阵V。eig(A)

ans =

9.3174 + 3.7436i

9.3174 - 3.7436i

-0.6347

>> [V,D]=eig(A)

V =

-0.3730 + 0.3936i -0.3730 - 0.3936i 0.5607

0.3343 + 0.3483i 0.3343 - 0.3483i -0.8119

0.6876 0.6876 0.1625

matlab实验习题

D =

9.3174 + 3.7436i 0 0

0 9.3174 - 3.7436i 0

0 0 -0.6347

6、求diag(A)

>> diag(A)

ans =

4

5

9

7、求tril(A)

tril(A)

ans =

4 0 0

7 5 0

3 4 9

8、求triu(A)

triu(A)

ans =

4 2 -6

0 5 4

0 0 9

9、repmat(A,2,3)

repmat(A,2,3)

ans =

4 2 -6 4 2 -6 4 2 -6

7 5 4 7 5 4 7 5 4

matlab实验习题

3 4 9 3 4 9 3 4 9

4 2 -6 4 2 -6 4 2 -6

7 5 4 7 5 4 7 5 4

3 4 9 3 4 9 3 4 9

10、flipud(A)

flipud(A)

ans =

3 4 9

7 5 4

4 2 -6

11、fliplr(A)

fliplr(A)

ans =

-6 2 4

4 5 7

9 4 3

12、rot90(A,3)

rot90(A,3)

ans =

3 7 4

4 5 2

9 4 -6

13、sum(A)

sum(A)

ans =

14 11 7

14、cumsum(A,1)和cumprod(A,2)

cumsum(A,1)

matlab实验习题

ans =

4 2 -6

11 7 -2

14 11 7

>> cumprod(A,2)

ans =

4 8 -48

7 35 140

3 12 108

15、B=magic(3)

B =

8 1 6

3 5 7

4 9 2

(1)求解AX=B；%写出三种方法

x=A\B

x =

-4.0312 -2.5156 0.6875

7.4687 4.7344 0.6875

-1.5312 -0.2656 -0.3125

>> x=inv(A)*B

x =

-4.0312 -2.5156 0.6875

7.4688 4.7344 0.6875

-1.5312 -0.2656 -0.3125 x=mldivide(A,B)

x =

-4.0312 -2.5156 0.6875

7.4687 4.7344 0.6875

matlab实验习题

-1.5312 -0.2656 -0.3125

(2)求解XA=B; %写出三种方法x=B/A

x =

-4.0469 5.3438 -4.4063

1.2031 -1.1563

2.0938

4.9531 -4.6563

5.5938

>> x=B*inv(A)

x =

-4.0469 5.3437 -4.4062

1.2031 -1.1563

2.0938

4.9531 -4.6563

5.5937

>> x=mrdivide(A,B)

x =

0.5833 -1.6667 1.0833

0.6472 -0.1444 0.5639

0.0222 1.3556 -0.3111

16、reshape(C,4,2)

c=[1 9 3 4;-1 -4 -3 -2]

c =

1 9 3 4

-1 -4 -3 -2

>> reshape(c,4,2)

ans =

1 3

-1 -3

9 4

-4 -2

matlab实验习题

2.17

A=[0 pi/3;pi/6 pi/2]

A =

0 1.0472

0.5236 1.5708

>> B=[sin(0) sin(pi/3);sin(pi/6) sin(pi/2)]

B =

0 0.8660

0.5000 1.0000

>> C=[cos(0) cos(pi/3);cos(pi/6) cos(pi/2)]

C =

1.0000 0.5000

0.8660 0.0000

>> I=B*B+C*C

I =

1.8660 1.3660

1.3660 1.8660

>> d=eig(A)

d =

-0.2940

1.8648

>> [M,L]=eig(A)

M =

-0.9628 -0.4896

0.2703 -0.8719

matlab实验习题

L =

-0.2940 0

0 1.8648

>> M*sin(L)*inv(M)

ans =

-0.1200 0.6048

0.3024 0.7873

>> funm(A,'sin')

ans =

-0.1200 0.6048

0.3024 0.7873

实验五

3.7

k=input('输入一个结束值:'); x=0;

for i=1:k

y=1;

for j=1:i

y=y*j;

end

x=x+y;

end

disp('级数值为：'),x

matlab实验习题

3.8

A=[];

for i=1:5

for j=1:5

if i==j

A=(i,i)=5; elseif abs(i-j)==1

A(i,j)=1; else A(i,j)=0;

end

end

End

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