matlab sistemas de matrices y vectores
TRANSCRIPT
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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.
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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:
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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:
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>> 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
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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
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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
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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 :
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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 ).
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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 .
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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
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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
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( ), 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= + +
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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 :
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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
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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 :
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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\
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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)
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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);
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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
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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
− =
−
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E MATLAB A B:
>> A = [1 1 1; 1 0 -1; -1 1 1];
>> B = [180;35;20];
Y :
>> x = linsolve(A,B)
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 :
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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 :
>> x = linsolve(A,B)
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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