Repeating matrix multiplication linear system

Hello, I am trying to do a matrix multiplication with a loop, I have a matrix A

A =

         0              0             45       
         1/25           0              0       
         0             39/100          3/10

and a vector

x =

      2000       
       100       
        25

Well, I do the multiplication

A*x

ans =

      1125       
        80       
        93/2

But then I want to do A*ans

A*ans

ans =

      4185/2     
        45       
       903/20

And I want to repeat this 50 times. My problem that I am running into is when I write a for loop, then it will only select the element. I don't know how to set an instance of a vector, here is what I have tried so far.

e = 2000;
l = 100;
a = 25;
x = [e; l; a];
for t = 0:50
    if t == 0
    PopulationInfo = A*x
    else
    PopulationInfo = A*PopulationInfo;
end

But this can't go anywhere because if I do A*x(t) it will just be an element of x, not the entire vector. Also, I want to do a plot starting at t=0 (the initial e, l, and a are populations at t=0), but with this loop there is no 0th element of an array.

[Sara]

what do you mean "then it will only select the element"?

[Rick]

e stands number for eggs, l stands for larva, and a is for adults. I want a plot of the number of eggs vs. t for t = 1:50, as well as number of adults and number of larva.

The formula is that e(t+1) = A*e(t), l(t+1) = A*l(t), and a(t+1) = A*a(t). The values for e,l, and a are at t=0.

Answer 1

[Azzi Abdelmalek]

A =[ 0     0     45       
     1/25  0      0       
     0   39/100 3/10]
e = 2000;
l = 100;
a = 25;
x = [e; l; a];
for t = 1:50
   x(:,t+1) = A*x(:,t);
end
t = 0:1:50;
plot(t,x)

[Rick]

Thanks, but how do I plot the elements of populatonInfo vs. t?

[Sara]

Using Joseph answer (below), you can do

t = 0:1:50;
plot(t,x(1,:),'r',t,x(2,:),'b',t,x(3,:),'g')

Answer 2

[Joseph Cheng]

to store each iteration of t.

e = 2000;
l = 100;
a = 25;
x = [e; l; a];
for t = 0:50
    x(:,t+2) = A*x(:,t+1);
end

Answer 3

[Rick]

Here is the code

e = 2000;
l = 100;
a = 25;
x = [e; l; a];
PopulationInfo = A*x;
for t = 1:50
      PopulationInfo = A*PopulationInfo;
end
for t = 0:50
    x(:,t+2) = A*x(:,t+1);
end
t = 0:1:50;
plot(t,x(1,:),'r',t,x(2,:),'b',t,x(3,:),'g');

But I get the error

Error using plot
Vectors must be the same lengths.

[Sara]

t = 0:1:51;

[Rick]

Thanks sara. Let's say I was trying to do it the way Azzi first mentioned (which was closer to what I came up with myself), how would I do it then?

[Sara]

Azzi has modified his answer to include the plotting. What you don't like?

[Rick]

didn't see the edit, thank u to Azzi and Sara and everyone here!