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MATLAB . MATrix LABoratory. :

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MATLAB;

MATLAB . , , , ...

MATLAB :

help

help topic

help command

help help help

helpwin o help

1.1. MATLAB

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lookfor keyword , keyword

F1 .

()! :

;

, _;

MATLAB .. one OnE ;

MATLAB 31 ;

, MATLAB . ; .

, . .

:

ans : default

( answer);

pi : = 3.1415926;

eps : = 2.2204e-016,

;

Inf inf : , ;

NaN nan : ;

i : ;

:

who: ;

whos: ,

;

1.2.

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clear: , ans

;

clear name: name;

clc: ;

clf: ;

:

abs (x) - | log10 (x) - 10 sin (x) - | rem (x,y) - cos (x) - | round (x) - tan (x) - | sqrt (x) - exp (x) - x | imag (x) - log (x) - | real (x) - , :

2+4+6. Enter.

2 + 4 + 6

ans =

12

MATLAB . : (4*25) + (6*22) - (2*99) :

4*25+6*22-2*99

ans = 34

A,B C MATLAB:

A=2

A =

2

B=4;

C=6

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C =

6

D=A+B+C

D =

12

E=B*25+C*22-A*99

E =

34

A,B C 2,4 6 . , MATLAB . , , . :

C

C =

6

, who.

who Your variables are: A B C

:

1.1

/ \ 56/8 = 8\56

^ 5^2

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! MATLAB . MATLAB 1x1 . , , - N:1 - 1:N.

: 24 52 65 1 ... 27 68

:

1

2

3

4

n-1

n

. ( ), . : 0.1. , (-). :

x= [0 0.1*pi 0.2*pi 0.3*pi 0.4*pi 0.5*pi 0.6*pi 0.7*pi 0.8*pi 0.9*pi pi]

x =

Columns 1 through 7

0 0.3142 0.6283 0.9425 1.2566 1.5708 1.8850

Columns 8 through 11

2.1991 2.5133 2.8274 3.1416

, ( ).

, :

y=sin(x)

y =

Columns 1 through 7

0 0.3090 0.5878 0.8090 0.9511 1.0000 0.9511

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Columns 8 through 11

0.8090 0.5878 0.3090 0.0000

2-D plot(x,y), x y .

11 . , . MATLAB 1, 0. , :

x(3) % x

ans

0.6283

y(5) % y

ans =

0.9511

% . .

1 5:

x(1:5)

ans =

0 0.3142 0.6283 0.9425 1.2566

1.3. , x y

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, . , , ( 1 , 2 ), .

x(2:2:7)

ans =

0.3142 0.9425 1.5708

, .

y(3:-1:1)

ans =

0.5878 0.3090 0

x(1:5) :

x(5:-1:1)

ans =

1.2566 0.9425 0.6283 0.3142 0

- MATLAB , - (;).

c = [1 ; 2 ; 3 ; 4 ; 5]

c =

1

2

3

4

5

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' - - , . -, -. 1:2 1 2 1.

a = 1:5

a =

1 2 3 4 5

b =a'

b =

1

2

3

4

5

:

1.2.

x = start:end

- x start,

1 end

x = start:increment:end

- x start,

increment

end end

linspace(start,end,number) - x start,

end, number

length(x) x

y=x' x

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1.2 ( .* ):

A = 2:6

A =

2 3 4 5 6

A + 5

ans =

7 8 9 10 11

B = -1:1:3

B =

-1 0 1 2 3

A .* B

ans =

-2 0 4 10 18

5 ( 2) ( 2).

linspace(A(1),B(5),length(A))

ans =

2.0000 2.2500 2.5000 2.7500 3.0000

:

A = [2, 5, 7, 1, 3];

B = [0, 6, 5, 3, 2];

A >= 5

ans =

0 1 1 0 0

A >= B

ans =

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1 0 1 0 1

:

A = [2, 5, 7, 1, 3, 4];

odds = 1 : 2 : length(A)

odds =

1 3 5

A(odds)

ans =

2 7 3

! MATLAB . , MATLAB . MATLAB :

A=[1 2 3; 4 5 6; 7 8 9]

A =

1 2 3

4 5 6

7 8 9

. a

A(3,3)=0

A =

1 2 3

4 5 6

7 8 0

0 . ,

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( ) .

A(2,6)=1

A =

1 2 3 0 0 0

4 5 6 0 0 1

7 8 0 0 0 0

, B.

A=[1 2 3;4 5 6; 7 8 9] ;

A =

1 2 3

4 5 6

7 8 9

B=A(3:-1:1, 1:3)

B =

7 8 9

4 5 6

1 2 3

, .

( ) :

ones(n) - nxn

ones(m,n) - mxn

zeros(n) - nxn

zeros(m,n) - mxn

rand(n) - nxn 0

1

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rand(m,n) - mxn 0

1

size(A) - mxn , [m,n]

length(A) -

.

.

z = zeros(2,3)

z =

0 0 0

0 0 0

rand(2,3)

ans =

0.9501 0.6068 0.8913

0.2311 0.4860 0.7621

>> SpoenaMatrica = [z, ans, ones(2,4)]

SpoenaMatrica =

0 0 0 0.9501 0.6068 0.8913 1.0000 1.0000 1.0000 1.0000

0 0 0 0.2311 0.4860 0.7621 1.0000 1.0000 1.0000 1.0000

,

, :

, N:M M:K

. ,

.. .

,

MATLAB.

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1.3

MATLAB

a + b a + b

a - b a - b

( ) a x b a .* b

a x b a * b

( ) a b a ./ b

a b a / b

ab a .^ b

: 1.3.

A B .

A = ones(2,3) * pi

A =

3.1416 3.1416 3.1416

3.1416 3.1416 3.1416

B = rand(2,3)

B =

0.3922 0.1712 0.0318

0.6555 0.7060 0.2769

C = A + B - ones(2,3)

C =

2.5338 2.3128 2.1734

2.7971 2.8476 2.4185

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.

A .* C

ans =

7.9602 7.2658 6.8280

8.7873 8.9461 7.5980

, NxM MxK .

A * C

??? Error using ==> mtimes

Inner matrix dimensions must agree.

C(3,1) = 2

C =

2.5338 2.3128 2.1734

2.7971 2.8476 2.4185

2.0000 0 0

A * C

ans =

23.0307 16.2119 14.4260

23.0307 16.2119 14.4260

, .

A .* C

??? Error using ==> times

Matrix dimensions must agree.

. , 1.3. ,

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.

MATLAB

. ,

:

{

:

[

] [

] [

]

:

1.)

: MATLAB :

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

b = [10; 5; -1];

x = inv(A) * b

x =

-2.0000

5.0000

-6.000

inv(A) MATLAB

, nxn.

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2.)

: MATLAB :

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

b = [10; 5; -1];

x = \b % b/A

x =

-2.0000

5.0000

-6.000

.

inv(A) - , nxn

:

eye(n) - nxn

eye(n,m) - nxm

rank(A) -

det(A) -

* ,

*

* .

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1.1. MATLAB: N , 0 2, N . y 2xN y , x . x . : N

N = 11;

N x- 0 2

x = linspace(0, 2*pi, N)

x =

0 0.6283 1.2566 1.8850 2.5133 3.1416 3.7699 4.3982 5.0265 5.6549 6.2832

y

y = cos(x)

y =

1.0000 0.8090 0.3090 -0.3090 -0.8090 -1.0000 -0.8090 -0.3090 0.3090 0.8090 1.0000

2xN y , x

= [y; x]

A =

1.0000 0.8090 0.3090 -0.3090 -0.8090 -1.0000 -0.8090 -0.3090 0.3090 0.8090 1.0000

0 0.6283 1.2566 1.8850 2.5133 3.1416 3.7699 4.3982 5.0265 5.6549 6.2832

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x

= (1:2, N:-1:1)

A =

1.0000 0.8090 0.3090 -0.3090 -0.8090 -1.0000 -0.8090 -0.3090 0.3090 0.8090 1.0000

6.2832 5.6549 5.0265 4.3982 3.7699 3.1416 2.5133 1.8850 1.2566 0.6283 0

. x x, y y. , :

plot(x,y)

1.4. , 0 2, 11

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1.2. MATLAB: ,

:

a)

{

b)

{

c)

{

d)

{