Q:

How to populate a matrix using for loop

C is a 2 by 360 matrix that forms outline of a unit circle. C = [v1|v2|v3... v360] where v1 is e rotated by 1◦, v2 is e rotated by 2◦ etc. R is a given rotation matrix. e is a column vector [1 0]
I initialized the matrix by
>> C=zeros(2,360);

I don't know how use the for loop to populate the entries of matrix C
>> for c = 1:360
C = (R^c)*e;
end

And then the following is supposed to plot the circle.
>> plot(C(1,:), C(2,:))

A:

You need to set each column at each rotation, so you will need to set C(:,c) at each rotation. ie
for c = 1:360
    C(:,c) = (R^c) * c;
end

However, you can do the whole thing without a for loop. (MATLAB likes avoiding for loops).
Since
t = 2*pi/360;
R = [cos(t) -sin(t); sin(t) cos(t)];

we have that
R*e = [cos(t); sin(t)];

So we're looking for
C = [cos(t) cos(2*t) ... cos(360*t);
     sin(t) sin(2*t) ... sin(360*t)];

ie
C = [cos(t * (1:360)); sin(t * (1:360))];

