This preview shows page 1. Sign up to view the full content.
Unformatted text preview: A and E3 A. What eﬀect did each of the Ei matrices have on the rows of
A? Create E4 so that its eﬀect on A is to multiply the bottom row by −6. How would you
extend this idea to matrices with more than two rows?
3. In the small village of Pedimaxus in the country of Sasquatchia, all 150 residents get one of the
two local newspapers. Market research has shown that in any given week, 90% of those who
subscribe to the Pedimaxus Tribune want to keep getting it, but 10% want to switch to the
Sasquatchia Picayune. Of those who receive the Picayune, 80% want to continue with it and
20% want switch to the Tribune. We can express this situation using matrices. Speciﬁcally,
let X be the ‘state matrix’ given by
where T is the number of people who get the Tribune and P is the number of people who get
the Picayune in a given week. Let Q be the ‘transition matrix’ given by
Q= 0.90 0.20
0.10 0.80 such that QX will be the state matrix for the next week. 490 Systems of Equations and Matrices
View Full Document