Matrices: word problem, transition matrix

[IrinaK.]

Homework Statement

Hello!
Please, take a look at the problem described in the attached file.
The question is: Explain why the transition matrix does what we want it to do.

Homework Equations

The Attempt at a Solution

(sorry, I don't know yet how to type formulas)
I don't quite understand this transition matrix.
0.90 0.20
0.10 0.80

I assume that the first column refers to Tribune readers and second one to Picayune readers.
Then the fist row should refer to those who are loyal to T and P, respectively; and second row - to those who would like to switch.
But textbook option suggests a different view.
Please, help me to understand this matrix.

Thank you!

 

[qspeechc]

When you multiply QX what type of matrix do you get? How do you perform the multiplication? Say QX=Y, write out what is Y.

By the way, to type in formulae, look here
https://www.physicsforums.com/threads/physics-forums-faq-and-howto.617567/#post-3977517

So for Q you would do
$$\begin{pmatrix} 0.90 & 0.20\\ 0.10 & 0.80 \end{pmatrix}$$
To see how you get that, just quote this post.

 

[IrinaK.]

When you multiply QX what type of matrix do you get? How do you perform the multiplication? Say QX=Y, write out what is Y.

By the way, to type in formulae, look here
https://www.physicsforums.com/threads/physics-forums-faq-and-howto.617567/#post-3977517

So for Q you would do
$$\begin{pmatrix} 0.90 & 0.20\\ 0.10 & 0.80 \end{pmatrix}$$
To see how you get that, just quote this post.

Thank you for reply. I don't understand how and why this matrix was formed in the first place (as I have stated in my questions); that is why given data is reflected in this particular manner.
As to multiplication, if I have understood that correctly, we can't multiply 2x2 matrix (which is Q in this case) by 1x1 matrix (X).
I would be grateful for the help.
Thank you!

 

[qspeechc]

X is not a 1x1 matrix, it's 2x1. X is
$$\begin{pmatrix}<br /> T\\<br /> P<br /> \end{pmatrix}$$
That is, the top number is T, the number of people who get the Tribune, and the bottom number Q is the number that get the Picayune.So you can multiply Q and X, because Q is 2x2.

It looks like you need to revise matrix multiplication. How would you multiply
$$\begin{pmatrix}<br /> 1 & 2\\<br /> 3 & 4<br /> \end{pmatrix}$$
with
$$\begin{pmatrix}<br /> 5\\<br /> 6<br /> \end{pmatrix}$$
If you can do that, then you can multiply Q and X, it's just that X has letters instead of numbers

 

[IrinaK.]

Yes, thank you. I've figured this out. Thank you for the help!
Just to show that I understand it now:

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