# Thread: HELP, i have no idea how to figure this out.

1. ## HELP, i have no idea how to figure this out.

(B), (C) and (D)

2. ## Re: HELP, i have no idea how to figure this out.

I don't know what a state matrix is. Do you have a definition?

3. ## Re: HELP, i have no idea how to figure this out.

I would guess that we are looking to find $\displaystyle \lim_{n \to \infty} P^n S_0$. For example: Solution to part a.

-Dan

4. ## Re: HELP, i have no idea how to figure this out.

Originally Posted by topsquark
I would guess that we are looking to find $\displaystyle \lim_{n \to \infty} P^n S_0$. For example: Solution to part a.

-Dan
Therein lies my confusion. I would guess that we are looking to find:
$$\lim_{n \to \infty} S_0 P^n$$

For example, Solution to part a.

5. ## Re: HELP, i have no idea how to figure this out.

Originally Posted by SlipEternal
Therein lies my confusion. I would guess that we are looking to find:
$$\lim_{n \to \infty} S_0 P^n$$

For example, Solution to part a.
Interesting. I had assumed that the initial S's would be a vertical matrix. Have to see what the OP has to say.

-Dan

6. ## Re: HELP, i have no idea how to figure this out.

It could be either way. I would expect that paola0889's text book would say which convention was being used.

7. ## Re: HELP, i have no idea how to figure this out.

this is what my textbook has, my calculus professor is horrible at teaching and we go by what the website explains
but it doesn't make sense

8. ## Re: HELP, i have no idea how to figure this out.

but thank you all for answering, I'm just going to leave it blank

9. ## Re: HELP, i have no idea how to figure this out.

A
Originally Posted by paola0889

this is what my textbook has, my calculus professor is horrible at teaching and we go by what the website explains
but it doesn't make sense
You were asked about whether your text book uses the convention that applying the matrix, A, to the vector, v, is Av, with v a column matrix, or vA with v as a row matrix. When you say "this is what my text book has" do you mean that your text book says nothing about what a "state matrix" is or how the multiplication is defined? It just has that problem even though nothing has been said about "matrices" before?

10. ## Re: HELP, i have no idea how to figure this out.

Based on the text:

$$Q = \begin{pmatrix}0.2 & 0.2 \\ 0.3 & 0.3\end{pmatrix}$$

$$F = (I-Q)^{-1} = \begin{pmatrix}0.8 & -0.2 \\ -0.3 & 0.7\end{pmatrix}^{-1} = \begin{pmatrix}1.4 & 0.4 \\ 0.6 & 1.6\end{pmatrix}$$

$$FR = \begin{pmatrix}0.36 & 0.64 \\ 0.44 & 0.56\end{pmatrix}$$

This means that:

$$\bar{P} = \begin{pmatrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0.36 & 0.64 & 0 & 0 \\ 0.44 & 0.56 & 0 & 0\end{pmatrix}$$

Now, it is still an open question about if the multiplication is with row vectors or column vectors.