(a)
To find the number of subscribers in 1st year.
(a)
Answer to Problem 6PS
The matrix is-
Explanation of Solution
Given Information:
The percentage changes in satellite subscriptions each year by the competing companies Gold and Galaxy and the non-subscribers respectively from company to company is given by the element in the matrix:
The following matrix represents the total number of subscribers and non-subscribers of the companies Gold and Galaxy.
The total number of subscribers each company will have 1 in year is found by the multiplication of the percentage subscribers of the company with the total number of subscribers of each company.
The percentage of subscribers in the company is found by the transpose of the given matrix of percentage subscription.
So,
The percentage of subscribers of a company and the non-subscribers is given by the matrix:
Thus, the total number of subscribers can be found by the multiplication of the matrices N and A.
So,
Hence, the total number of subscribers each company will have 1 in year is given by the matrix.
b.
To find the number of subscribers in 2nd year.
b.
Answer to Problem 6PS
The matrix is-
Explanation of Solution
The total number of subscribers each company will have 2 in years is found by the multiplication of the percentage subscribers of the company with the total number of subscribers of each company in 1 year.
Thus, the total number of subscribers can be found by the multiplication of the matrices N1 and A.
So,
Hence, the total number of subscribers each company will have 1 in year is given by the matrix.
c.
To find the number of subscribers after 3rd year.
c.
Answer to Problem 6PS
Explanation of Solution
The total number of subscribers each company will have 3 in years is found by the multiplication of the percentage subscribers of the company with the total number of subscribers of each company in 2 years.
Thus, the total number of subscribers can be found by the multiplication of the matrices N2 and A.
So,
Hence, the total number of subscribers each company will have 1 in year is given by the matrix.
The number of non-subscribers is decreasing each year.
d.
To find how does the number of subscribers vary each year.
d.
Answer to Problem 6PS
Explanation of Solution
The number of subscribers in each year is increasing year by year.
The number of non-subscribers is decreasing each year.
Chapter 8 Solutions
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