Matlab sistemas de Matrices y Vectores

8/16/2019 Matlab sistemas de Matrices y Vectores

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AC AAB

CAE . 2

1. E EA GA

E N. 2 S MATLAB . M

. T ( ,

).

2. DCC

MATLAB . E MATLAB

, ,

. E MATLAB (

).

3. DEFC DE ACE ECE

L , ,

. P , . S

(H Z)

. L , ,

:

1 :

H: 8 T , 4 T , 12 T Z: 6 T , 3 T , 12 T .

2 :

H: 10 T , 6 T , 5 T

Z: 9 T , 5 T , 4 T

3 :

H: 7 T , 8 T , 5 T

Z: 7 T , 0 T , 5 T .

4 :

H: 11 T , 7 T , 0 T

Z: 11 T , 6 T , 5 T .

E . A

T 1 2.


2/23

T 1. I H T 2. I Z

L M A L M A

1 S 6 2 10 1 S 6 3 12

2 S 8 4 3 2 S 9 5 4

3 S 5 6 3 3 S 7 0 5

4 S 9 5 0 4 S 11 6 0

E , () (). C .

E , , :

11 12 13

21 22 23

31 32 33

41 42 43

LevaduraMalta

Agua

Fila 1, Semana1

Fila 2, Semana 2

Fila 3, Semana 3

Fila 4, Semana 4

|| |

a a aa a aa a a

a a a

− − − − − − − −− − − − − −

− − − −↓ ↓ ↓

→ →

= →

→

A

E T 1 2,

,

. E , ,

, , , , .

A ,

MATLAB.

E MATLAB . S

(MATLAB , ). L

;

(;). P , H

T 1 H:

>> H = [6 2 10; 8 4 3; 5 6 3; 9 5 0]

L :

H =

6 2 10

8 4 3

5 6 3

9 5 0

A H , W:


3/23

E W : H 43 ( ), 10. M Z, .

4. DECCAE DE ACE

Y MATLAB, . D M (

) .

C , H, 0 7 T. C ?

P , ( 4 3, ) 7. E :

>> H(4,3)=7

E :

H =6 2 10

8 4 3

5 6 3

9 5 7

P , 7S , ( H) , , , .

A, , C H,

. S T 1, , :

T 1. I H

L

1 S 6

2 S 8

3 S 5

P , MATLAB:


4/23

>> parcial = H(1:3,1)

E :

parcial =

6

8

5

L : 1 3 H:

parcial = H(1:3,1)

O , H .

E HL :

>> agua = H(:,3)

E :

agua =

10

3

3

7

L : 3 H:

parcial = H(:,3)

D (

:

>> semana2 = H(2,:)

E :

semana2 =

8 4 3

P T 1 .

C 1

F 1 3

C 3

T F


5/23

F, [ ]. P , 1 4 H ( , : ):

>> H([1 4],:)

E :

ans =

6 2 10

9 5 7

F, H(:) H .

5. DEFC DE ECE E AAB

C , MATLAB. E , .

U ( ) ( ). V 4, 1, 2, 3 4. C Z :

L M A

1 1 S 6 3 122 2 S 9 5 43 3 S 7 0 54 4 S 11 6 0

C , . L ( 4 , ):

>> z1 = [6 3 12];

>> z2 = [9 5 4];

>> z3 = [7 0 5];

>> z4 = [11 6 0 3];

C , .

6. DECCAE DE ECE

S , , , (. H(1,3)). C , ( 1).

P , , Z 0 5 .

E, 4:

>> z4(3)=7


6/23

E :

z4 =

11 6 7 3

7. BAD DE EEE

E 4 , . E []:

>> Z(3) =[]

E :

z4 =

11 6 7

E 4 [].

8. CCAEAC DE ACE

E MATLAB . E .

P , 1, 2, 3, 4 Z, Z . E :

>> Z = [z1; z2; z3; z4]

E :

Z =

6 3 12

9 5 4

7 0 5

11 6 7

N , .

C , MATLAB H Z . E , , . E , , .

S :

>> [H Z]

E :

ans =

6 2 10 6 3 12

8 4 3 9 5 4

5 6 3 7 0 5

9 5 7 11 6 7


7/23

S :

>> [H;Z]

E :

ans =

6 2 10

8 4 35 6 3

9 5 7

6 3 12

9 5 4

7 0 5

11 6 7

9. DEFC DE ECE AD D

A , .

C MATLAB, S(), . N MATLAB Y =()

Y . . E . S, , MATLAB .

S , , . H , A , .

A , , X=[0 0.1 0.2 ] 6, , . P . C

:

>> x=[0:2*pi]

E :

x =

0 1 2 3 4 5 6

L : X 0 2* (MATLAB =3.1416). MATLAB 2* ( , ).

S , :

>> plot(x,sin(x))

Y :


8/23

L , . V :

>> x=[0:0.1:2*pi];

S , W 63 , 6.2.

L 0 2*, MATLAB 1 1, 0.1 ( = [0 0.1 0.2 0.3 0.4 6.2].

A :

>> plot(x,sin(x))

Y :

E (63 ).


9/23

10. ACE EDEFDA

E MATLAB . A :

(4) (44)

(3,5) (35)

(4) (44)

(3) (33)

(2,4) (24)

(1,2,) 1 2

(1,2,) 10^1 10^2.

(2,5) 0 1, , (25)

(5) 0 1, , (55)

(4) (44), , 0 1.

(4,3) (43), , 0 1.

(4) (44) . E

2.

11. FAC DE A A A A DE A

MATLAB ,

:

( ),

.

A , :

A=() A

=(A) A

(A) A

(A) A

90(A,)G *90 A . . S , =1

(A) A

(A) A

(A,,)C A A

. S A .


10/23

A , :

>> A = rand(3)

>> B = diag(diag(A))

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

E , C (66)

(33). A , . L .

12. BEE FAC BE ACE

A . P :

(A) A

()

13. EADE AC

MATLAB . L MATLAB :

1. AAB

+

*

^

\

/

.*

./

.\

.^

(A). A.

A H Z

S , H 2

,

. S 2 , :

>> H = H+2


11/23

E :

H =

8 4 12

10 6 5

7 8 5

11 7 9

S

. P

, :

V S. E MATLAB, :

>> Suma = H + Z

E :

Suma =

14 7 24

19 11 9

14 8 10

22 13 16

P , . P

:

>> Resta = H - Z

E :

Resta =

2 1 0

1 1 1

0 8 0

0 1 2

H H Z. L

, ( 1 3

, 3 4, ). E


12/23

( ), H Z . P

. E Z

H .

A, 5

H, H. E , H:

>> producto = 5*H

E :

producto =

40 20 60

50 30 25

35 40 25

55 35 45

A (H AG M ). A

: ,

?. L

:

E P,

( , , , ,

, H AG M .):

50 55136 12780 79

P

=

D MATLAB:

>> P =[50 55; 136 127; 80 79];

A . E

.

E , :

( ) ( ) ( )*$ *$ *$Costo semana levadura levadura malta malta agua agua= + +


13/23

E , (H Z) . H

H:

C H H AG:

1 : (8 )*(50 $/ )+ (4 )*(136 $/ ) +(12 )*(80$/ ) =1904

2 : (10 )*(50 $/ )+ (6 )*(136 $/ ) +(5 )*(80$/ ) =1716

3 : (7 )*(50 $/ )+ (8 )*(136 $/ ) +(5 )*(80$/ ) =1838

4 : (11 )*(50 $/ )+ (7 )*(136 $/ ) +(9 )*(80$/ ) =2222

C H .:

1 : (8 )*(55 $/ )+ (4 )*(127 $/ ) +(12 )*(79$/ ) =1896

2 : (10 )*(55 $/ )+ (6 )*(127 $/ ) +(5 )*(79$/ ) =1707

3 : (7 )*(55 $/ )+ (8 )*(127 $/ ) +(5 )*(79$/ ) =1796

4 : (11 )*(55 $/ )+ (7 )*(127 $/ ) +(9 )*(79$/ ) =2205

E . V H P

( H AG

.):

8 4 12 8* 4* 12* 8* 4* 12*10 6 5 10* 6* 5*

50 136 80 19045050 136

55 127 79 18965555 12710* 6* 5 79*

* *7 8 5 7

80136

50 1* 6* 5* 7* 8* 5*11

36 807 9 11* 7* 9* 11* 7* 9

12755 127 79

7955 127 7

80* 950 136 80

K H P

+ + + + + + + + = = = = + + + + + + + +

1716183822

1707179622022 5

E MATLAB :

>> K=H*P

E :

K =

1904 1896

1716 1707

1838 1796

2222 2205

A H P, H*P, (

) . E , H

(, ) P .

L H*P :

• E H ( ) H ( ).

• E P ( )

P ( ).

D H AG

, M :


14/23

C ( ),

H M .

S (

). P :

>> sum(K)

E :

ans =

7680 7604

E , , $7.680 HAG $7.604 M .

.

A: A , ,

. S ,

.

E MATLAB (') . T

( ).

P , K, :

>> T = K'

E :

T =

1904 1716 1838 2222

1896 1707 1796 2205

P K T K T ( T K). S (T) T, K:

>> sum(T)

E :

ans =

3800 3423 3634 4427

1796


15/23

14. EE ACA DE ACE

A , MATLAB.

EE 1

C :

.) C () ,

S 12 ( ) :

.) C ?

S :

E M ; 7476

EE 2

L VST A L . S , ,

. L ( )

3 :


16/23

E . C

?

E :

R:

L ( ) :

E R AG .

15. EADE AA A EC DE EA DE ECACE EAE

MATLAB . P , . C ,

A =

, A . L 2 :

= (A)*

= A\


17/23

A , ( \) . E , ( ) . C E , .

EE 3

E

, ,

. H

, . D

, . E

. C M ,

. P ,

3 4

1 2 M

− =

−

S :

AAE A

R

0. P , :

1 10 19 2 11 20 3 12 21 4 13 22

5 14 23 6 15 24 7 16 25 8 17 26 9 18 27

E 1, 21, 1, 18, 22, 5, 14, 0, 26, 1.

D MATLAB:

>> m=[1 21 1 18 22 5 14 0 26 1]

E :

m =

1 21 1 18 22 5 14 0 26 1

E ( M,

, 2 ). M :

>> length(m)


18/23

E :

ans =

10

P , 25. P :

>> m = reshape(m,2,5)

E :

m =

1 1 22 14 26

21 18 5 0 1

V M MATLAB:

>> M=[-3 4; -1 2];

M:

>> c=M*m

E :

c =

81 69 -46 -42 -74

41 35 -12 -14 -24

E :

>> c = reshape(c,1,10)

E :

ans =

81 41 69 35 -46 -12 -42 -14 -74 -24

C 81, 41, 69, 35, 46, 12, 42, 14, 74, 24.

N :

M* =

E M , , . E

.

D 81, 41, 69, 35, 46, 12, 42, 14, 74, 24.

>> c=[81 41 69 35 -46 -12 -42 -14 -74 -24];

R ( M):

>> c = reshape(c,2,5);


19/23

D M MATLAB:

>> M=[-3 4; -1 2];

H =M\:

>> m=M\c;

R :

>> m=reshape(m,1,10)

m =

1 21 1 18 22 5 14 0 26 1

R ( ):

1 21 1 18 22 5 14 0 26 1

EECC

L MATLAB:1,9,10,22,24,43,16,37,53,24,36,56,16,28,44,37,17,34,21,18,20,25,18,31,1,20,20

P ,

1 0 10 1 10 1 2

M

=

16. FC E()

L MATLAB

\.

L A= :

= (A,)

E

EE 4

U 110 , , 1/8 1/9 1/5

15. L 65. C ?

L :

1. U 10 , :

V + C + T = 110 V , C T .2. 1/8 1/9 1/5 15:

(1/8)*V +(1/9)*C + (1/5)*T = 153. L 65

V + T = 65


20/23

E A = B, :

V x C

T

=

E :

( ) ( ) ( )

1* 1* 1* 110

1 8 * 1 9 * 1 5 * 151* 0* 1* 65

V C T

V C T V C T

+ + =

+ + = + + =

1 1 1 110

1 8 1 9 1 5 * 151 0 1 65

V

C T

=

E MATLAB A B:

>> A = [1 1 1; 1/8 1/9 1/5; 1 0 1];

>> B = [110;15;65];

Y :

>> x = linsolve(A,B)

S

x =

40

45

25

E 40 , 45 25 .

EE 5

L 180. E 35 20 . H .

L :

4. L 180.G + M + P = 180 G , M P .

5. E 35G = 35 + P G P=35

6. E 20 P = 20 + (G M) G + M + P = 20

E A = B, :

G x M

P

=

E :

1* 1* 1* 1801* 0* 1* 351* 1* 1* 20

G M P G M P G M P

+ + = + − =

− + + =

1 1 1 1801 0 1 * 351 1 1 20

G M P

− =

−


21/23

E MATLAB A B:

>> A = [1 1 1; 1 0 -1; -1 1 1];

>> B = [180;35;20];

Y :


S

x =

80

55

45

E 80, 55 45.

EECC 2

S :

E 40 , , . L . E . A , .

EE 6

LEY DE KIRCHHOFF DE LA CORRIENTE: L .

LEY DE KIRCHHOFF DEL VOLTAJE: L .

U E ( ) , , .

O . L .

S E = 10 V 1 2 3

3 , 4 5 R R y R= Ω = Ω = Ω

L :


22/23

1. L A . S . E:

1 2 3 0i i i− − =

2. L 1 L .

1 1 2 2 1 1 2 20 E R i R i R i R i E − − = → + =

3. L 2 L .

3 3 2 2 2 2 3 30 0 R i R i R i R i− = → − + =

E A = B, :

1

2

3

i x i

i

=

E :

1 2 3

1 1 2 2 3

1 2 2 3 3

1* 1* 1* 0* * 0*

0* * * 0

i i i R i R i i E

i R i R i

− − = + + = − + =

1

1 2 2

2 3 3

1 1 1 00 *

00

i R R i E

R R i

− − =

−

R 1 2 310 3 , 4 5 E V R R y R= = Ω = Ω = Ω :

1

2

3

1 1 1 03 4 0 * 100 4 5 0

iii

− − =

−

E MATLAB A B:

>> A = [1 -1 -1; 3 4 0; 0 -4 5];

>> B = [0;10;0];

Y :


S

x =

1.9149

1.0638

0.8511

E 1 2 31.9149 , 1.0638 , 0.8511i A i A i A= = =

EECCS :

C 1 2 3, ,i i i E = 6V

1 2 3 43 , 5 , 4 2 R R R y R= Ω = Ω = Ω = Ω .


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Matlab sistemas de Matrices y Vectores

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