
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 8th, 2017, 04:32 PM  #1 
Newbie Joined: Mar 2015 From: Penns Posts: 8 Thanks: 0  Markov Chain Discrete Dynamical System
Hey guys, so my teacher told us to look at the book and find a very similar problem and to just do it. I don't typically ask for the answer but I just need help setting up this problem. A drug is administered @ 100 units of the drug into the blood. Every 10 minutes, 50% of the drug goes to bloodstream & 50% to liver During this same time period 75% of the drug in the liver goes to the bloodstream while 25% stays in the liver. Initially injection gets process started 100 units of the drug directly to blood stream(0 to liver). How to model this system given x sub k = amount in blood stream after 10 min time interval. y sub k = amount of drug in the liver after k 10 min time intervals have passed. Using matrix algebra: X(k+1) = A * X(k)[X is a vector] where X(k)= Matrix x sub k over y sub k. Then there is another matrix showing A = (2x2) matrix top 2 values are 1/2 & 3/4. Bottom 2 values are 1/2 and 1/4. Can any one tell me what the hell is going on? I think I can use the markov chain or the matrix algebra. I'm super lost and a step by step is appreciated. 
May 8th, 2017, 04:56 PM  #2 
Senior Member Joined: Sep 2015 From: CA Posts: 1,265 Thanks: 650 
if I understand this what you have is $\begin{bmatrix}b_{n+1} \\l_{n+1}\end{bmatrix}=\begin{bmatrix}0.5 &0.75\\0.5 &0.25\end{bmatrix}\begin{bmatrix}b_n \\ l_n\end{bmatrix}$ $\begin{bmatrix}b_0 \\ l_0\end{bmatrix}=\begin{bmatrix}100 \\ 0\end{bmatrix}$ 
May 8th, 2017, 05:35 PM  #3  
Newbie Joined: Mar 2015 From: Penns Posts: 8 Thanks: 0  Quote:
That is correct. It's a bit confusing saying find all the eigen values & bases for all eigenspaces of the matrix A. I get eigenvalues and all. But it's confusing in the form of a word problem. I think you help me set it up tho.  

Tags 
chain, discrete, dynamical, markov, system 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Topology equivalence in dynamical system  eric_h22  Differential Equations  0  March 31st, 2015 06:08 AM 
Discrete markov chain  kfp22  Advanced Statistics  0  October 8th, 2014 06:43 AM 
Markov chain  butabi  Advanced Statistics  1  February 12th, 2012 04:20 PM 
Eigenvalues of Jacobian of dynamical system  agsmith87  Real Analysis  0  February 9th, 2012 09:02 PM 
discrete dynamical systems  alpacino  Applied Math  0  April 26th, 2009 06:48 AM 