How to iteratively multiply a vector by a matrix iteratively

I want to multiply an initial vector p_t0 by a matrix P. The vector and matrix are specified below. If I simply do p = p_t0*P I get my first set of answers which is what I want but I want to repeat the procedure 50 times (for t=[1 50]). Any ideas on how I can do this? I attempted it below but kept getting an error saying "the number of elements in A and B must be the same."

h = 0.5;
u = 0.3; 
P = [1-h h 0 0 0 ; ... 
     u 1-h-u h 0 0; ... 
     0 u 1-h-u h 0; ...
     0 0 u 1-h-u h; ...
     0 0 0 u 1-u;];
%Initialize initial probability vector 
p0_t0 = 0.2;
p1_t0 = 0.2;
p2_t0 = 0.2;
p3_t0 = 0.2;
p4_t0 = 0.2;
p_t0 = [p0_t0 p1_t0 p2_t0 p3_t0 p4_t0];

p = p_t0*P %initial vector produced at time of 0 
tf = 50
for t = 2:tf+1
    p(1) = p_t0*P
    p(t) = p(t-1)*P;
end

Answer 1

[Roger Stafford]

The the product p_t0*P produces a five-element vector so you should write:

   ......
   p = zeros(tf,5); % <-- for more efficient allocation
   p(1,:) = p_t0*P;
   for t = 2:tf
     p(t,:) = p(t-1,:)*P;
   end