1 семестр / Линейная Алгебра / 23_Кучеренко Антон_Модуль 2_Индивидуальное задание

Задание 1

>> subplot(2,2,1)

>> plot([4 7],[-6 6],'b','linewidth',2)

>> hold on

>> plot([1 4],[-2 -6],'k','linewidth',2)

>> plot([7 1],[6 -2],'k','linewidth',2)

>> axis equal

>> hold on

>> grid on

>> text(1,1,'A(1;-2)')

>> line([-10 10],[0 0],'color','black')

>> line([0 0],[-10 10],'color','black')

>> text(1,1,'B(4;-6)')

>> text(1,1,'C(7;6)')

>> plot(1,-2,'blueo','linewidth',3)

>> plot(4,-6,'blueo','linewidth',3)

>> plot(7,6,'blueo','linewidth',3)

>> line([4 5],[-6 -2],'color','k','linewidth',4)

>> line([4 8],[-6 -7],'color','red','linewidth',4)

>> plot(5,-2,'k^','linewidth',3)

>> plot(8,-7,'r>','linewidth',3)

>> title('4x-y-22=0')

>> subplot(2,2,2)

>> grid on, hold on

>> line([-10 10],[0 0],'color','black')

>> line([0 0],[-10 10],'color','black')

>> plot([1 4],[-2 -6],'k','linewidth',2)

>> plot([7 1],[6 -2],'k','linewidth',2)

>> plot([4 7],[-6 6],'k','linewidth',4)

>> text(1,1,'B(4;-6)')

>> text(1,1,'C(7;6)')

>> text(1,1,'A(1;-2)')

>>line([1 4.45],[-2 -4.15],'color','b','linewidth',2)

>> line([1 3.5],[-2 -3.5],'color','k','linewidth',4)

>> plot(3.5,-3.5,'k>','linewidth',3)

>> line([1 2],[-2 2],'color','r','linewidth',3)

>> plot(2,2,'r^','linewidth',3)

>> title('x+4y+7=0')

>> subplot(2,2,3)

>> grid on, hold on

>> line([-10 10],[0 0],'color','black')

>> line([0 0],[-10 10],'color','black')

>> plot([1 4],[-2 -6],'k','linewidth',2)

>> plot([7 1],[6 -2],'k','linewidth',2)

>> plot([4 7],[-6 6],'k','linewidth',2)

>> plot(5.5,0,'bo','linewidth',3)

>> text(1,1,'M(5,5;0)')

>> line([1 5.5],[-2 0],'color','b','linewidth',2)

>> line([1 4],[-2 -0.65],'color','k','linewidth',4)

>> plot(4,-0.65,'black>','linewidth',3)

>> line([1 0.3],[-2 2],'color','r','linewidth',4)

>> plot(0.3,2,'r^','linewidth',3)

>> title('2x-4,5y-11=0')

>> subplot(2,2,4)

>> grid on, hold on

>> line([-10 10],[0 0],'color','black')

>> line([0 0],[-10 10],'color','black')

>> plot([1 4],[-2 -6],'k','linewidth',2)

>> plot([7 1],[6 -2],'k','linewidth',2)

>> plot([4 7],[-6 6],'k','linewidth',2)

>> text(1,1,'B(4;-6)')

>> text(1,1,'C(7;6)')

>> text(1,1,'A(1;-2)')

>> plot(1,-2,'blueo','linewidth',3)

>> plot(4,-6,'blueo','linewidth',3)

>> plot(7,6,'blueo','linewidth',3)

>> line([1 1.2],[-2 -3.6])

>> line([1 1.2],[-2 -1.6])

>> line([1 5],[-2 -2],'linewidth',3)

>> plot(5,-2,'bo','linewidth',3)

>> text(1,1,'Q(5;-2)')

>> line([1 3],[-2 -2],'linewidth',3,'color','black')

>> plot(3,-2,'k>','linewidth',3)

>> plot(1,2,'r^','linewidth',3)

>> line([1 1],[-2 2],'linewidth',3,'color','r')

>> title('y+2=0')

>> format rational

>> p=-17/sqrt(17)

p =

-2177/528

>> q=184/(10*sqrt(17))

q =

2151/482

>> subplot(2,2,2)

>> plot(q,p,'bo','linewidth',3)

>> text(1,1,'H(2151/482; -2177/528)')

Дополнительное задание.

1)|AH|=|p(A(1;-2),L)|=|-1/(√17)+2/(√17)-7/(√17)|=6/(√17)≈4,1231,

где L: x+4y+7=0; λ=√17

2)BC: x+4y+7=0

(x-4)/(-1)=(y+6)/4

y=4x-22

x/5,5-y/22=1

AH: x+4y+7=0

(x-1)/4=(y+2)/(-1)

y=-x/4-7/4

-x/7-y/(7/4)=1

AM: 2x-4,5y-11=0

>> box on

>> grid on, hold on

>> plot3(3,1,-2,'blacko','linewidth',3)

>> plot3(2,-5,2,'blacko','linewidth',3)

>> line([-10 10],'color','black')

??? Error using ==> line

Not enough input arguments.

>> line([-10 10],[0 0],[0 0],'color','black')

>> line([0 0],[-10 10],[0 0],'color','black')

>> line([0 0],[0 0],[-10 10],'color','black')

>> xlabel('x'),ylabel(

??? xlabel('x'),ylabel(

|

Error: Expression or statement is incorrect--possibly unbalanced (, {, or [.

>> y

??? Undefined function or variable 'y'.

>> xlabel('x'),ylabel('y'),zlabel('z')

>> line[8 -2],[-1 3],[-5 1],'color','black','linewidth',3)

??? line[8 -2],[-1 3],[-5 1],'color','black','linewidth',3)

|

Error: Unbalanced or unexpected parenthesis or bracket.

>> line([8 -2],[-1 3],[-5 1],'color','black','linewidth',3)

>> line([1 3],[-8 -2],[0 4],'color','black','linewidth',3)

>> line([0 5],[0 2],[0 3],'color','red','linewidth',3)

>> A=-5,B=-7,C=13,D=48,

A =

-5

B =

-7

C =

13

D =

48

>> x = -10:0.4:10; y = -10:0.5:10;

>> [X,Y]=meshgrid(x,y);

>> Z = (-A*X-B*Y-D)/C;

>> figure

>> hold on

>> plot3(X,Y,Z,'or','MarkerSize',4)

>> plot3(-2,5,-2,'blacko','linewidth',3)

>> line([-3 -1],[2 8],[-4 0],'color','black','linewidth',3)

>> A=-5,B=-7,C=13,D=51,

A =

-5

B =

-7

C =

13

D =

51

>> Z = (-A*X-B*Y-D)/C;

>> plot3(X,Y,Z,'or','MarkerSize',4)

>> A=-5,B=-7,C=13,D=51,

A =

-5

B =

-7

C =

13

D =

51

>> x = -10:0.4:10; y = -10:0.5:10;

>> plot3(X,Y,Z,'or','MarkerSize',4)

>> line([-3 -1],[2 8],[-4 0],'color','black','linewidth',3)

>> line([8 -2],[-1 3],[-5 1],'color','black','linewidth',3)

>> D=30

D =

30

>> Z = (-A*X-B*Y-D)/C;

>> plot3(X,Y,Z,'or','MarkerSize',4)

>> line([8 -2],[-1 3],[-5 1],'color','black','linewidth',3)

>> line([-3 -1],[2 8],[-4 0],'color','black','linewidth',3)

>> HOLD ON

Warning: Could not find an exact (case-sensitive) match for 'HOLD'.

C:\Program Files\MATLAB\R2010b\toolbox\matlab\graphics\hold.m is a case-insensitive match

and will be used instead.

You can improve the performance of your code by using exact

name matches and we therefore recommend that you update your

usage accordingly. Alternatively, you can disable this warning using

warning('off','MATLAB:dispatcher:InexactCaseMatch').

This warning will become an error in future releases.

??? Error using ==> hold at 71

Unknown command option.

>> hold on

>> D=51

D =

51

>> Z = (-A*X-B*Y-D)/C;

>> plot3(X,Y,Z,'or','MarkerSize',4)

>> plot3(X,Y,Z,'or','MarkerSize',4)

>> line([-3 -1],[2 8],[-4 0],'color','black','linewidth',3)

>> line([8 -2],[-1 3],[-5 1],'color','black','linewidth',3)

>> D=48

D =

48

>> Z = (-A*X-B*Y-D)/C;

>> plot3(X,Y,Z,'or','MarkerSize',4)

>> line([8 -2],[-1 3],[-5 1],'color','black','linewidth',3)

>> line([-3 -1],[2 8],[-4 0],'color','black','linewidth',3)

>>

>>

>>

>>

>>

>>

>>

>>

>>

>>

>>

>> A=5,B=7,C=-13,D=-51,

A =

5

B =

7

C =

-13

D =

-51

>> Z = (-A*X-B*Y-D)/C;

>> plot3(X,Y,Z,'or','MarkerSize',4)

>> line([8 -2],[-1 3],[-5 1],'color','black','linewidth',3)

>> line([-3 -1],[2 8],[-4 0],'color','black','linewidth',3)

>> D=-48;

>> Z = (-A*X-B*Y-D)/C;

>> plot3(X,Y,Z,'or','MarkerSize',4)

>> line([8 -2],[-1 3],[-5 1],'color','black','linewidth',3)

>> line([-3 -1],[2 8],[-4 0],'color','black','linewidth',3)

>> D=-48;

>>

>>

>>

>>

>>

>>

>>

>>

>>

>>

>>

>> A=12;B=15;C=-30;D=111;

>> Z = (-A*X-B*Y-D)/C;

>> plot3(X,Y,Z,'or','MarkerSize',4)

>> line([8 -2],[-1 3],[-5 1],'color','black','linewidth',3)

>> line([-3 -1],[2 8],[-4 0],'color','black','linewidth',3)

>>

>>

>>

>>

>>

>>

>>

>>

>>

>>

>>

>> A=8;B=15;C=-14;D=67;

>> Z = (-A*X-B*Y-D)/C;

>> plot3(X,Y,Z,'or','MarkerSize',4)

>> line([8 -2],[-1 3],[-5 1],'color','black','linewidth',3)

>> line([-3 -1],[2 8],[-4 0],'color','black','linewidth',3)

>> A=8;B=15;C=-14;D=67;

>> A=8;B=15;C=-14;D=87;

>> Z = (-A*X-B*Y-D)/C;

>> plot3(X,Y,Z,'or','MarkerSize',4)

>> line([8 -2],[-1 3],[-5 1],'color','black','linewidth',3)

>> line([-3 -1],[2 8],[-4 0],'color','black','linewidth',3)

>>

>> A=-5;B=-7;C=13;D=-48;

x=-10:0.5:10;

y=-10:0.5:10;

[X Y]=meshgrid(x,y);

Z=(-A*X-B*Y-D)/C;

plot3(X,Y,Z,'Markersize',5)

surf(X,Y,Z)

hold on

X1=[-10 10];

Y2=3*(X1+2)+5;

Z2=2*(X1+2)-2;

Y1=2*(X1-3)/5+1;

Z1=3*(X1-3)/5-2;

plot3(X1,Y1,Z1)

plot3(X1,Y2,Z2)

>> A=-5;B=-7;C=13;D=-48;

x=-10:0.5:10;

y=-10:0.5:10;

[X Y]=meshgrid(x,y);

Z=(-A*X-B*Y-D)/C;

plot3(X,Y,Z,'Markersize',5)

surf(X,Y,Z)

hold on

X1=[-10 10];

Y2=3.*(X1+2)+5;

Z2=2.*(X1+2)-2;

Y1=2.*(X1-3)/5+1;

Z1=3.*(X1-3)/5-2;

plot3(X1,Y1,Z1)

plot3(X1,Y2,Z2)

>> A=-5;B=-7;C=13;D=-48;

x=-10:0.5:10;

y=-10:0.5:10;

[X Y]=meshgrid(x,y);

Z=(-A*X-B*Y-D)/C;

plot3(X,Y,Z,'Markersize',5)

surf(X,Y,Z)

hold on

X1=[-10 10];

Y2=3.*(X1+2)+5;

Z2=2.*(X1+2)-2;

Y1=2.*(X1-3)./5+1;

Z1=3.*(X1-3)./5-2;

plot3(X1,Y1,Z1)

plot3(X1,Y2,Z2)

>>