/

7

:

1) 2) 3)

: . , , .

:

1) ( mean) :

>> x=[1 3 5 7 3];>> mean(x)

ans =

3.8000

2) ( median) : , , , .

>> x=[1 3 5 7 3 5 4 7];>> median(x)

ans =

4.5000

3) ( range) :

>> x=[1 3 5 7 3 5 4 7];>> range(x)

ans =

6

4) ( var) :

>> x=[1 3 5 7 3 5 4 7];>> var(x)

ans =

4.2679

5) ( std) :

>> x=[1 3 5 7 3 5 4 7]; >> std(x)

ans = 2.0659

6) ( skewness) :

7) ( kurtosis) :

>> x=[1 3 5 7 3 5 4 7];>> skewness(x)

ans =

-0.1218

>> kurtosis(x)

ans =

2.0811

Matlab , . , , . :

>> x=[1 2 3;4 5 6;7 8 9] x = 3x3 1 2 3 4 5 6 7 8 9

>> x=[1 2 3 4] ( 1x4)x =

1 2 3 4

>> x=[1; 2; 3; 4] ( 4x1)x =

1 2 3 4

( ) :

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

x =

1 2 3 4 5 6 7 8 9

x . >> x'

ans =

1 4 7 2 5 8 3 6 9

, 2 , , / (.*). / , :

x x , ( * ) , x, ij i- j- . :

ij=i11j+22j++j

!! .

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

A =

1 3 2 4 7 9 2 3 6>> B=[2 5 1;3 7 4;6 2 9]

B =

2 5 1 3 7 4 6 2 9>> C=A*B

C =

23 30 31 83 87 113 49 43 68 :>> C_el=A.*B

C_el =

2 15 2 12 49 36 12 6 54 2 , / CC_el *.*

-1 ( inv) : , -1 *-1= -1* = . >> A=[1 2 1;1 -1 1;1 1 0]

A =

1 2 1 1 -1 1 1 1 0

>> inv(A)

ans =

-0.3333 0.3333 1.0000 0.3333 -0.3333 0 0.6667 0.3333 -1.0000

: nxn, 1 0 ( eye).

>> eye(3)

ans =

1 0 0 0 1 0 0 0 1

( det) : ( ) , ( ), . , , . 2x2 ( 2 )

2x2

|| :

3x3

3x3 ( 3 ) 3x3 : : , 3x3 , || . .

:>> A=[2 3 -1;4 1 2;1 -1 1]

A =

2 3 -1 4 1 2 1 -1 1

>> det(A)

ans =

5

>> inv(A)

ans =

0.6000 -0.4000 1.4000 -0.4000 0.6000 -1.6000 -1.0000 1.0000 -2.00001) 02) >> A=[2 3 1;4 1 5;1 -1 2]

A =

2 3 1 4 1 5 1 -1 2

>> det(A)

ans =

0

>> inv(A)Warning: Matrix is singular to working precision.

ans =

Inf Inf Inf Inf Inf Inf Inf Inf Inf

( eig):

x . , i :| -i | = 0

, ( eye) | -iI | -iI. E, o , j, rj=[r1;r2;..;r], :

(-j) rj = 0

0, , .H atlab eig.

: : >> A=[1 3 2;4 7 9;2 3 6]

A =

1 3 2 4 7 9 2 3 6 =eig(A) , :>> E=eig(A)

E =

13.0385 -0.3956 1.3571 :[V,D]=eig(A), Matlab V D . >> [V,D]=eig(A)

V =

-0.2854 -0.9291 -0.6587 -0.8497 0.3470 -0.4701 -0.4433 0.1278 0.5875D =

13.0385 0 0 0 -0.3956 0 0 0 1.3571

: a1x1+a 2x2 ++ anxn=b, ai xi , n . ai b . m n , , m n mxn. x=b, , : \.: ( x=[x1 ; x2 ;x3]):

x1+2x2+x3=-1x1-x2+x3=3x1+x2=4

, =[1 2 1; 1 -1 1;1 1 0] b=[-1;3;4] (3x3) det(A)=30

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

A =

1 2 1 1 -1 1 1 1 0

>> b=[-1;3;4]

b =

-1 3 4

, Matlab, :x=A\b

>> x=A\b

x =

5.3333 -1.3333 -3.6667 o : x1 = 5.3333 x=[x1;x2;x3] : x2 = -1.3333 x3 = -3.6667 , det(A)0.

: , . ? 2+3+=2 : A*x=b => 4++5=3 -+2=1

= [2 3 1;4 1 5;1 -1 2] , x=[;;] b=[2;3;1]. >> A=[2 3 1;4 1 5;1 -1 2]

A =

2 3 1 4 1 5 1 -1 2>> b=[2;3;1]

b =

2 3 1

>> x=A\bWarning: Matrix is singular to working precision.

x =

-Inf Inf Inf>> det(A)

ans =

0 : , ( ).

( trapz) :

, a,b

f(x) , . , , . [a,b] n : x =(ba)/n :x0=a, x1=a+x, x2=a+ 2x ,..., xi=a+ix,..., xn=a+nx=b, , :

f(x) , f(x1), f(x2),,f(xn), x1, x2,,xn , f(x) [x1 , xn] trapz(x,y), :

x=[x1;x2;;xn] y=[f(x1);f(x2);;f(xn)]

:

:

>> x = [0 0.1 0.25 0.33 0.46 0.59 0.64 0.78 0.99];>> y = [1.14 13.45 33.99 54.68 55.5 70.0 76.3 81.19 109.7];>> plot(x,y,-o)

To :

>> trapz(x,y)ans = 57.8787

....