Need matrix help on this problem please

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In summary, in a community of 100,000 adults, there is a 90% probability that subscribers to a concert series will renew their subscription and a 0.2% probability that non-subscribers will subscribe for the next season. With a present number of 1200 subscribers, it is possible to predict stability over the next three seasons. By calculating the determinant of the matrix, it is determined that there will be a 0.898 probability of stability, which is close to the 90% probability of subscribers renewing their subscription. This suggests that there will be little change in the number of subscribers over the next three seasons.
  • #1
LakeMountD
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in a community of 100,000 adults, subscribers to a concert series tend to renew their subscription with a probability 90% and persons not subscribing will subscribe for the next season with probability 0.2%. If the present number of subscribers is 1200, can one predict an increase or decrease or stability over each of the next three seasons?

This is in the matrix section so I am assuming we have to use one but have no idea what they want?!
 
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  • #2
If you write the number of people who subscribed last year as X and the number of people who did not as Y, then the expected number of people to subscribe this year is 0.90X+ 0.002Y. Of course, the number of people who will not subscribe this year will be 0.10X+ 0.998Y. You can write that as a matrix: What matrix multiplied by the column vector (X,Y) will give the vector (0.90X+ 0.002Y, 0.10X+ 0.998Y)?

The easiest way to answer that question is to look at the determinant of the matrix.
 
  • #3
determinent of the matrix would be

[ .9 * .998] - [.002 * .10] correct?
 
  • #4
Yes. What is that equal to and what does it tell you?
 
  • #5
= .898 .. not really sure what that is telling me though. honestly my differential equations teacher is so bad that i have to learn everything on google. pretty sad when your 5,000 dollars in tuition is going towards research you have to do on your own on google to learn everything but hey.

im assuming that since .898 is so close to .90 or 90% that its saying things are going to be stable. This right?

also how do you get a vector out of those numbers?
 
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1. What is a need matrix?

A need matrix is a tool used in decision-making and problem-solving to prioritize needs and determine the most effective solutions. It is usually represented in a grid or table format, with needs listed on one axis and potential solutions listed on the other axis.

2. How do I create a need matrix?

To create a need matrix, start by identifying the specific problem or decision you need to address. Then, list all the relevant needs associated with the problem. Next, brainstorm and list potential solutions for each need. Finally, assign a score or weight to each need and solution based on their level of importance or effectiveness. This will help you determine the best solution for the problem.

3. What are the benefits of using a need matrix?

Using a need matrix can help you systematically analyze a problem and make data-driven decisions. It can also help you prioritize needs and allocate resources effectively. Additionally, a need matrix can facilitate communication and collaboration among team members by providing a visual representation of the problem and potential solutions.

4. Are there any limitations to using a need matrix?

While a need matrix can be a useful tool, it is important to keep in mind that it is only as effective as the information and data used to create it. If the needs or solutions are not accurately identified or weighted, the resulting decisions may not be optimal. It is also important to regularly review and update the need matrix as new information becomes available.

5. How can I use a need matrix in my research or work?

A need matrix can be used in various fields and industries, such as business, education, healthcare, and social services. It can aid in project planning, resource management, and decision-making processes. By utilizing a need matrix, you can improve the efficiency and effectiveness of your research or work by prioritizing needs and identifying the most suitable solutions.

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