Chapter 4.1, Problem 52E

Tourism in the 1990s Referring to the 1998 tourism figures given in Exercise 51, assume that the following (fictitious) figures represent the corresponding numbers from 1988:

To	Australia	South Africa
From North America	500	100
Europe	900	800
Asia	1,400	50

Take A to be the $3\times 2$ matrix whose entries are the 1998 tourism figures, and take B to be the $3\times 2$ matrix whose entries are the 1988 tourism figures.

a. Compute the matrix $A-B$. What does this matrix represent?

b. Assuming that the changes in tourism over 1988–1998 are repeated in 1998–2008, give a formula (in terms of A and B) that predicts the number of visitors from the three regions to Australia and South Africa in 2008.