Need Help to Homework

Hello,

Consider the matrix A=[2/3 -2/3; 2/3 7/3].
Consider 10000 equally spaced points on the unit circle in R2 (assume Euclidian
distance). The coordinates of each of these points define a column vector
v in R2. Compute w = Av for all points, interprete the resulting vectors
again as points in the plane, and draw all resulting points in one figure.

What i need to do?

[Wayne King]

Unless you show some sample code where you have tried something, it's best to ask your professor or the TA for help to get started.

[Alex]

My problem is that I can not understand the condition of the problem Can you tell me what I need, in principle, to find.

Random points with coordinates X and Y for the vector space V in R2, as I understand it can be generated using the rand (2, n), where n is any number ... Then I looked at the theory of how to calculate the distance to the Euclidean plane R2 ... dist = sqrt ((x2-x1) ^ 2 + (y2-y1) ^ 2) .... And now, as I understand it should be part of this circle of 10000 points with the same distance between them, ie dist1 = dist2 = ..... = dist10000. But maybe I misunderstood?

I think the generation of these points and will be the first part of the solution. Then, as I see the coordinates located at equal distance from each other points should be written in the vector V, with which multiplication and perform on a given matrix A, and the vector W. .. But again, I'm not sure I understand correctly the problem conditions

Answer 1

[Matt J]

My hint would be to use the LINSPACE command to generate equally spaced angles theta for the points. There is nothing in the homework exercise that asks for random points, so I'm not sure why you mention it.

Answer 2

[Wayne King]

My hint would be this:

1.) Think about what equation every point on the unit circle satisfies in terms of cos(theta) and sin(theta).

2.) Generate 10,000 equally-spaced angles between [0,2*pi]

I think any more help than that and I'm just writing the code for your assignment.

[Alex]

so correctly?

clear all

clc

n = 10000;

theta = rand(2,n)*(2*pi);

r = rand(2,n);

x =r.*cos(theta);

y =r.*sin(theta);

plot(x,y,'.')

[Wayne King]

I think your assignment says "on the unit circle", so r = 1. You're not generating points on or inside the unit circle.

 n = 10000;
 theta = linspace(0,2*pi,1e4); %sorry I misread earlier
 r = 1; % or just leave it off.
 x =r.*cos(theta);
 y =r.*sin(theta);
 plot(x,y,'.')

 v = [x;y];

[Matt J]

It's early in the morning for me still, but I still don't see where the assignment "specifically asks for random points".

[Wayne King]

oh sorry, Matt is correct!! I'm trying to do too many things at once. You should follow Matt's suggestion then and generate an equally spaced vector from 0 to 2*pi. I'll edit my post, but leave comment to show that Matt correctly pointed out my mistake.

[Alex]

Thank you very much After reading, following your recommendations on linspaсe could not correctly place limits on the function. Thanks to you all now turns out)

Answer 3

[Image Analyst]

You might find the FAQ useful: http://matlab.wikia.com/wiki/FAQ#How_do_I_create_a_circle.3F