Question

The following table gives the number of people (in thousands) who visited Australia and South Africa in $1998^{6}$ : $$ \begin{array}{|l|c|c|} \hline & \text { To } & \text { Australia } & \text { South Africa } \\ \hline \text { From } & \text { North America } & 440 & 190 \\ \hline \text { Europe } & 950 & 950 \\ \hline \text { Asia } & 1,790 & 200 \\ \hline \end{array} $$ You predict that in $2008,20,000$ fewer people from North America will visit Australia and 40,000 more will visit South Africa, 50,000 more people from Europe will visit each of Australia and South Africa, and 100,000 more people from Asia will visit South Africa, but there will be no change in the number visiting Australia. a. Use matrix algebra to predict the number of visitors from the three regions to Australia and South Africa in 2008 . b. 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 2008 tourism figures. Give a formula (in terms of $A$ and $B$ ) that predicts the average of the numbers of visitors from the three regions to Australia and South Africa in 1998 and $2008 .$ Compute its value.

          The following table gives the number of people (in thousands) who visited Australia and South Africa in $1998^{6}$ :
$$
\begin{array}{|l|c|c|}
\hline & \text { To } & \text { Australia } & \text { South Africa } \\
\hline \text { From } & \text { North America } & 440 & 190 \\
\hline \text { Europe } & 950 & 950 \\
\hline \text { Asia } & 1,790 & 200 \\
\hline
\end{array}
$$
You predict that in $2008,20,000$ fewer people from North America will visit Australia and 40,000 more will visit South Africa, 50,000 more people from Europe will visit each of Australia and South Africa, and 100,000 more people from Asia will visit South Africa, but there will be no change in the number visiting Australia.
a. Use matrix algebra to predict the number of visitors from the three regions to Australia and South Africa in 2008 .
b. 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 2008 tourism figures. Give a formula (in terms of $A$ and $B$ ) that predicts the average of the numbers of visitors from the three regions to Australia and South Africa in 1998 and $2008 .$ Compute its value.

Added by Iker S.

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