# Tourism in the 1990s The following table gives the number of people (in thousands) who visited Australia and South Africa in 1998: 14 To Australia South Africa From North America 440 190 Europe 950 950 Asia 1,790 200 You estimate that 5% of all visitors to Australia and 4% of all visitors to South Africa decide to settle there permanently. Take A to be the 3 × 2 matrix whose entries are the 1998 tourism figures in the above table, and take B = [ 0.05 0.04 ] and C = [ 0.05 0 0 0.04 ] . Compute the products AB and AC . What do the entries in these matrices represent?

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### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
Publisher: Cengage Learning
ISBN: 9781337274203
BuyFind

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
Publisher: Cengage Learning
ISBN: 9781337274203

#### Solutions

Chapter
Section
Chapter 5.2, Problem 73E
Textbook Problem

## Tourism in the 1990s The following table gives the number of people (in thousands) who visited Australia and South Africa in 1998:14 To Australia South Africa From North America 440 190 Europe 950 950 Asia 1,790 200 You estimate that 5% of all visitors to Australia and 4% of all visitors to South Africa decide to settle there permanently. Take A to be the 3 × 2 matrix whose entries are the 1998 tourism figures in the above table, and take B = [ 0.05 0.04 ]   and   C = [ 0.05 0 0 0.04 ] .Compute the products AB and AC. What do the entries in these matrices represent?

Expert Solution
To determine

To calculate: The products AB and AC and what do the entries represent where A is the 3×2 matrix whose entries are 1998 tourism figures from the table and B=[0.050.04] C=[0.05000.04] and the table represents the number of people who visited Australia and South Africa and you estimated that 5% of all visitors to Australia and 4% of visitors to South Africa settle there permanently.

 To Australia South Africa From North America 440 190 Europe 950 950 Asia 1790 200

### Explanation of Solution

Given Information:

A is the 3×2 matrix whose entries are 1998 tourism figures from the table and B=[0.050.04] C=[0.05000.04] the table represents the number of people who visited Australia and South Africa and you estimated that 5% of all visitors to Australia and 4% of visitors to South Africa settle there permanently.

 To Australia South Africa From North America 440 190 Europe 950 950 Asia 1790 200

Formula used:

A matrix with m rows and n columns is of dimension m×n, where m and n are positive integers.

For matrices A with dimension m×n and B with dimension k×l, the product AB is defined if the number of columns in A equal number of columns in B, n=k.

For matrices A with dimension m×n and B with dimension n×k, the product AB is the matrix of dimension m×k and ijth entry of AB is the sum of product of corresponding entries of row i of A and column j of B.

Calculation:

Consider A is the 3×2 matrix whose entries are 1998 tourism figures from the table and B=[0.050.04] C=[0.05000.04] the table represents the number of people who visited Australia and South Africa and you estimated that 5% of all visitors to Australia and 4% of visitors to South Africa settle there permanently.

 To Australia South Africa From North America 440 190 Europe 950 950 Asia 1790 200

Write the table as a matrix A.

Thus, tourism in 1998 is A=[4401909509501,790200].

Consider, the product AB.

Recall that a matrix with m rows and n columns is of dimension m×n, where m and n are positive integers.

Since, number of rows in B=[0.050.04] is 2 and number of columns is 1,

Substitute 2 for m and 1 for n in m×n .

Thus, dimension of B=[0.050.04] is 2×1 .

Since, number of rows in A=[4401909509501,790200] is 3 and number of columns is 2,

Substitute 3 for m and 2 for n in m×n .

Thus, dimension of A=[4401909509501,790200] is 3×2 .

Since, number of rows in C=[0.05000.04] is 2 and number of columns is 2,

Substitute 2 for m and 2 for n in m×n .

Thus, dimension of C=[0.05000.04] is 2×2 .

Recall that for matrices A with dimension m×n and B with dimension n×k, the product AB is the matrix of dimension m×k and  ijth entry of AB is the sum of product of corresponding entries of row i of A and column j of B

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