Repeating matrix multiplication linear system

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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.
  2 Comments
Sara
Sara on 16 Jul 2014
what do you mean "then it will only select the element"?
Rick
Rick on 16 Jul 2014
Edited: Rick on 16 Jul 2014
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.

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Accepted Answer

Azzi Abdelmalek
Azzi Abdelmalek on 16 Jul 2014
Edited: Azzi Abdelmalek on 16 Jul 2014
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)
  2 Comments
Rick
Rick on 16 Jul 2014
Thanks, but how do I plot the elements of populatonInfo vs. t?
Sara
Sara on 16 Jul 2014
Using Joseph answer (below), you can do
t = 0:1:50;
plot(t,x(1,:),'r',t,x(2,:),'b',t,x(3,:),'g')

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More Answers (2)

Joseph Cheng
Joseph Cheng on 16 Jul 2014
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

Rick
Rick on 16 Jul 2014
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.
  4 Comments
Sara
Sara on 16 Jul 2014
Azzi has modified his answer to include the plotting. What you don't like?
Rick
Rick on 16 Jul 2014
didn't see the edit, thank u to Azzi and Sara and everyone here!

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