# How do I label the solution of a word problem using matrix multiplication?

The table on the left gives the birth and death rates (per million) by region. The table on the right gives the populations (in millions) in each region for a number of years. Use matrix multiplication to get a matrix showing the total number of births and deaths in each year. Births Deaths Africa .036 .014 Asia .019 .008 Latin America .021 .006 North America .014 .008 Europe .011 .011 years Africa Asia L.America N.America Europe 1960 283 1628 218 199 425 2002 839 3518 539 320 513

Thank you

-
If this is homework, please label it as homework. Even if it is not, it is highly impolite to post giving orders (your post is written in the imperative); if you have a question then ask a question, don't give commands. And in your haste to copy the text of the assignment, you failed to format it, so that there is no "table on the right" and no "table on the left". –  Arturo Magidin Feb 16 '11 at 5:32
As Arturo said, I don't see any tables and I don't know what you are asking. What have you tried? –  Ross Millikan Feb 16 '11 at 5:35

Suppose there are $R$ regions (in your case, $R = 5$) and $Y$ years (in your case, $Y = 2$). You have an $R \times 2$ matrix $A_{rs}$, where $A_{r1}$ is the birth rate in region $r$, and $A_{r2}$ is the death rate. You also have the region population $Y \times R$ matrix $B_{yr}$, which represents the population of region $r$ at year $y$. You want the total number of deaths and births for each year. This is a summation over the different regions of something, which corresponds to a multiplication of the two matrices (perhaps transposed).