SBurchette
  • SBurchette
Can one take the limit of a matrix as it is multiplied by itself infinite times? We are using a matrix to model how a population changes over a given period of time. Repeated multiplication of the matrix will show how the percentages change after each period of time transpires. The question was will the population stabilize. So I reasoned that if the limit of repeated multiplications of the matrix approached specific values, that the population would indeed stabilize.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Yes, you can do that. Look up Markov Matrix.
SBurchette
  • SBurchette
Example/ Matrix A represents how the population changes over a week. Matrix B represents the population. So\[\lim_{t \rightarrow \infty}(B)A^t\] Would represent the population after t numbers of weeks transpire. I took this limit numerically and the product matrix consistently approached particular values.
anonymous
  • anonymous
I'll explain.... are you familiar with diagonalization of a matrix?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

SBurchette
  • SBurchette
Not entirely, I'm in a elementary linear algebra class. We have just been covering matrix operations.
anonymous
  • anonymous
I see. I'm not quite sure how to explain it to you without referencing diagonalization or at least eigenvalues and eigenvectors, but you are correct in that if the rows and columns of the matrix add to 1 and all of the entries are positive, repeated multiplication by itself will approach a constant result
SBurchette
  • SBurchette
Ok, I suppose the question more of an application than a presentation of theory. I do anticipate diving deeper into matrix theory =) Thanks for the assistance.
anonymous
  • anonymous
What you stumbled on is actually a very deep result in matrix theory, it's just that you're not quite prepared to appreciate it yet. You'll get there soon, though.

Looking for something else?

Not the answer you are looking for? Search for more explanations.