Question

Referring to the 1998 tourism figures given in the preceding exercise, assume that the following (fictitious) figures represent the corresponding numbers from 1988 . $$ \begin{array}{|l|c|c|} \hline & \text { To } & \text { Australia } & \text { South Africa } \\ \hline \text { From } & \text { North America } & 500 & 100 \\ \hline \text { Europe } & 900 & 800 \\ \hline \text { Asia } & 1,400 & 50 \\ \hline \end{array} $$ 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 .

          Referring to the 1998 tourism figures given in the preceding exercise, assume that the following (fictitious) figures represent the corresponding numbers from 1988 .
$$
\begin{array}{|l|c|c|}
\hline & \text { To } & \text { Australia } & \text { South Africa } \\
\hline \text { From } & \text { North America } & 500 & 100 \\
\hline \text { Europe } & 900 & 800 \\
\hline \text { Asia } & 1,400 & 50 \\
\hline
\end{array}
$$
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 .

Added by Michael G.

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