Homework Help: Initial State Vector

1. Nov 29, 2012

alexcc17

1. The problem statement, all variables and given/known data
Suppose that the initial vector P0 is not given and instead we are given that at time t=299 the state vector is P_299=[.1 .1 .8].
Than find P_300, the state vector at time t=300

2. Relevant equations
I also know from the problem it is referencing that the transition matrix is:

[.3 .4 .3]
T= [.5 0 .5]
[.5 .5 0]

3. The attempt at a solution

I thought I would just set up the equation as such:

P_299=P0 * T^299

and just take the inverse of T^299 and multiply it by P_299 to get the P0, then use that to find P_300, but my graphing calculator won't even calculate the 299th power of the transition matrix, so there must be another way to do this.

Any help would be great!

2. Nov 30, 2012

haruspex

I don't see any need to worry about P0. T describes how the state changes from one timestamp to the next, right? And you know the state at time 299. And you want the state at time 300? Either I'm missing some subtlety or you are missing the obvious.

3. Nov 30, 2012

alexcc17

Would it just be p_299*T to get p_300?

4. Nov 30, 2012

HallsofIvy

Yes, that's what an exponent means isn't it? T300v= T(T299v)

5. Nov 30, 2012

alexcc17

Wasn't sure if that applied to matrices. Thanks