>> EXERCICE3

A=[3 -1 0;0 1 0;0 0 2]

A=

3 -1 0

0 1 0

0 0 2

>> B=[3 5 1;7 -2 4;-6 3 2]

B=

3 5 1

7 -2 4

-6 3 2

>> C=[5 6 5;6 10 9;5 9 10]

C=

5 6 5

6 10 9

5 9 10

>> a=eig(A)

a=

>> b=eig(B)

b=

-7.3538 + 0.0000i

5.1769 + 2.0832i

5.1769 - 2.0832i

>> c=eig(C)

c=

0.5660

1.9659

22.4681
>> [V,L]=eig(A)

V=

1.0000 0.4472 0

0 0.8944 0

0 0 1.0000

L=

3 0 0

0 1 0

0 0 2

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

V=

1.0000 0.4472 0

0 0.8944 0

0 0 1.0000

L=

3 0 0

0 1 0

0 0 2

>> A+C

ans =

8 5 5

6 11 9

5 9 12

>> A*C

ans =

9 8 6

6 10 9

10 18 20
>> A.*C

ans =

15 -6 0

0 10 0

0 0 20

>> v=[1;2;3]

v=

>> R=A+v

Error using +

Matrix dimensions must agree.

>> B=[3 5 1 1;7 -2 4 2;-6 3 2 3]

B=

3 5 1 1

7 -2 4 2

-6 3 2 3

>> k=null(B)

k=

0.1191

-0.0959

-0.6349

0.7573

>>EXERCICE4

>> A=[2 1 -3;1 -2 1];

>> b=[1 2]';

>> rank(A)

ans =

2
>> B=[2 1 -3 1;1 -2 1 2]

B=

2 1 -3 1

1 -2 1 2

>> rank(B)

ans =

>> c=[1 1 1]';

>> y=A*C

Undefined function or variable 'C'.

Did you mean:

>> y=A*c

y=

>> X=inv(A)*b

Error using inv

Matrix must be square.

>>EXO 6

>> A=[1 2 3;2 3 1;3 1 2]

A=

1 2 3

2 3 1

3 1 2

>> A([2 3],[1 3])

ans =

2 1

3 2

>> A([2 3],1:2)

2 3

3 1

>> A([2 3],:)

ans =

2 3 1

3 1 2

>> A([2 3],end)

ans =

>> A(:)

ans =

>> A(5)

ans =

>> reshape(A(:),size(A))

ans =
 1 2 3

2 3 1

3 1 2

>>>> % EXO7

>> A=[1 2 3; 2 3 1;3 1 2]

A=

1 2 3

2 3 1

3 1 2

>> C=[A,zeros(3,2);zeros(2,3),eye(2)]

C=

1 2 3 0 0

2 3 1 0 0

3 1 2 0 0

0 0 0 1 0

0 0 0 0 1

>>>> TP1

1)

>> A=magic(5)

A=

17 24 1 8 15

23 5 7 14 16

4 6 13 20 22

10 12 19 21 3

11 18 25 2 9

>> sum_lignes=sum(A,2)

sum_lignes =
 65

65

65

65

65

>> sum_colonnes=sum(A,1)

sum_colonnes =

65 65 65 65 65

>> sum_diagonale1=sum(diag(A))

sum_diagonale1 =

65

>> sum_diagonale2=sum(diag(fliplr(A)))

sum_diagonale2 =

65

>> A(3,:)

ans =

4 6 13 20 22

>> A(1,2)

ans =

24

>>2)

>> p=[3 -1 7]

p=

3 -1 7

>> roots(p)

ans =

0.1667 + 1.5184i

0.1667 - 1.5184i
>>

>> %plus a propose des matrices et tableaux

>> A=[10 7 8 7;7 5 6 7;8 6 10 9;7 5 9 10]

A=

10 7 8 7

7 5 6 5

8 6 10 9

7 5 9 10

>> b1=[32 23 33 31]'

>> b1 =

32

23

33

31

>> b2=[32.1 22.9 33.1 30.9]'

b2 =

32.1

22.9

33.1

30.9

>> x=inv(A)*b1

x=

1.000

1.000

1.000

1.000

>> x2=inv(A)*b2

x2 =

4.9048

-5.4762

2.7190
 -0.0524

>> y=eig(A)

y=

30.6789

3.3601

0.3157

0.6453

>> >>TP4

>> A=rand(7)

A=

0.8147 0.5469 0.8003 0.0357 0.6555 0.8235 0.7655

0.9058 0.9575 0.1419 0.8491 0.1712 0.6948 0.7952

0.1270 0.9649 0.4218 0.9340 0.7060 0.3171 0.1869

0.9134 0.1576 0.9157 0.6787 0.0318 0.9502 0.4898

0.6324 0.9706 0.7922 0.7577 0.2769 0.0344 0.4456

0.0975 0.9572 0.9595 0.7431 0.0462 0.4387 0.6463

0.2785 0.4854 0.6557 0.3922 0.0971 0.3816 0.7094

>> inv(A)

ans =

0.2150 0.3124 -0.5303 0.2803 0.9697 -0.5554 -0.7391

0.7551 0.6244 -0.6416 -0.6979 0.1878 1.9664 -2.7736

0.1938 -0.8510 -0.1891 0.3615 0.4972 0.4637 -0.1897

-1.2070 -0.0659 0.9475 0.6014 -0.0246 -1.1940 1.8149

0.2754 -0.5342 1.2076 -0.1488 -0.0479 -1.5358 1.5155

0.5698 0.4188 0.0176 0.3729 -1.2926 1.4092 -1.8184

-0.4570 0.1211 0.1233 -0.4794 -0.2533 -1.4436 3.5402

>> eye(A)

Error using eye

N-dimensional arrays are not supported.

>> inv(A)*A
ans =

1.0000 0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000

0.0000 1.0000 0.0000 -0.0000 0.0000 0.0000 0.0000

-0.0000 -0.0000 1.0000 0.0000 0.0000 0.0000 -0.0000

-0.0000 -0.0000 -0.0000 1.0000 -0.0000 -0.0000 -0.0000

0.0000 -0.0000 -0.0000 -0.0000 1.0000 -0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000

-0.0000 0.0000 -0.0000 0.0000 -0.0000 -0.0000 1.0000

>> [L,U,P]=lu(A,1)

Error using lu

Permutation flag must be 'matrix' or 'vector'.

>> [L,U,P]=lu(A)

L=

1.0000 0 0 0 0 0 0

0.1390 1.0000 0 0 0 0 0

0.9917 0.8497 1.0000 0 0 0 0

0.8920 0.4309 0.1411 1.0000 0 0 0

0.1068 0.9972 -0.5589 0.5457 1.0000 0 0

0.6923 0.9136 0.1090 0.4916 0.4693 1.0000 0

0.3049 0.4638 -0.2361 0.3868 0.4414 0.0716 1.0000

U=

0.9134 0.1576 0.9157 0.6787 0.0318 0.9502 0.4898

0 0.9430 0.2944 0.8396 0.7016 0.1850 0.1188

0 0 -1.0164 -0.5374 -0.4565 -0.4047 0.2086

0 0 0 -0.8557 0.3892 -0.0467 0.2480

0 0 0 0 -1.1244 -0.0479 0.4568

0 0 0 0 0 -0.7029 -0.3610

0 0 0 0 0 0 0.2825
P=

0 0 0 1 0 0 0

0 0 1 0 0 0 0

0 1 0 0 0 0 0

1 0 0 0 0 0 0

0 0 0 0 0 1 0

0 0 0 0 1 0 0

0 0 0 0 0 0 1

>> det(A)=prod(diag(U))*(-1)^P

Subscript indices must either be real positive integers or logicals.

det(A)=prod(diag(U))*(1)^P

Subscript indices must either be real positive integers or logicals.

>> [piv,L,U]=lu(A)

piv =

1.0000 0 0 0 0 0 0

0.1390 1.0000 0 0 0 0 0

0.9917 0.8497 1.0000 0 0 0 0

0.8920 0.4309 0.1411 1.0000 0 0 0

0.1068 0.9972 -0.5589 0.5457 1.0000 0 0

0.6923 0.9136 0.1090 0.4916 0.4693 1.0000 0

0.3049 0.4638 -0.2361 0.3868 0.4414 0.0716 1.0000

L=

0.9134 0.1576 0.9157 0.6787 0.0318 0.9502 0.4898

0 0.9430 0.2944 0.8396 0.7016 0.1850 0.1188

0 0 -1.0164 -0.5374 -0.4565 -0.4047 0.2086

0 0 0 -0.8557 0.3892 -0.0467 0.2480

0 0 0 0 -1.1244 -0.0479 0.4568

0 0 0 0 0 -0.7029 -0.3610

0 0 0 0 0 0 0.2825
U=

0 0 0 1 0 0 0

0 0 1 0 0 0 0

0 1 0 0 0 0 0

1 0 0 0 0 0 0

0 0 0 0 0 1 0

0 0 0 0 1 0 0

0 0 0 0 0 0 1
b=[1 2 3 4 5 6 7]';
y=zeros(size(b));
x=zeros(size(b));
%Foward substitution
for i=1:size(A,1)
y(i)=b(piv(i));
for j=1:i-1
y(i)=y(i)-L(i,j)*y(j);
end
end

TP2

1)
x=linspace(-2,2);
y=exp(x);
plot(x,y);
grid on
title('courbe exp(x)')
xlabel('x');
ylabel('y');
2)
R=3;
w=linspace(0,3*R);
x=R*(w-sin(w));
y=R*(1-cos(w));
plot(x,y);
hold on
grid on
xlabel('x')
ylabel('y')
title('trace de la courbe en cycloide');
3)
x=linspace(-10,10);
y=linspace(-10,10);
r=sqrt(x.*x+y.*y);
z=10.*cos(r)./r+2;
plot3(x,y,z)
grid('on')
hold('on')
xlabel('X')
ylabel('Y')
zlabel('Z')
title('trace de la courbe 3D')
3)

x=linspace(-0.1,0.1);

v=x.*sin(1./x);

>> plot(x,v,'r');

>> grid on

>> hold on

>> plot(x,-x,'b.')

plot(x,x,'b.')

>> xlabel('axe des x')

>> ylabel('axe des y')

>> gtext('y=x')

>> gtext('y=-x')

>> gtext('y=x*sin(1/x)')
>>