# Need matrix help on this problem please!

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?!

HallsofIvy
Homework Helper
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.

determinent of the matrix would be

[ .9 * .998] - [.002 * .10] correct?

HallsofIvy