Concept explainers
(a)
Matrix to represent the transitions in player ownership.
(a)
Answer to Problem 37PPS
Matrix for the transitions in player ownership:
Explanation of Solution
Given information:
From the stable population of 25,000 people,
17,252 own digital audio players and 7748 own portable CD players.
Let
xbe the number of people who own CD players.
And
y be the number of people who own digital audio players.
Now,
Express the situation wherein there is a change in player ownership:
Keeping or switching to CD players:
Keeping or switching to digital audio players:
Therefore,
Matrix for the above two system of equations:
(b)
Prediction for the number of people will own digital audio player next year.
(b)
Answer to Problem 37PPS
About 20,218 people will own digital audio player next year.
Explanation of Solution
Given information:
From the stable population of 25,000 people,
17,252 own digital audio players and 7748 own portable CD players.
Calculation:
Use the matrix from Part (a) to obtain the matrix equation:
Perform the multiplication:
Simplify:
Add the elements:
Therefore,
About 20,218 people will own digital audio player next year.
(c)
The number of people owned digital audio player last year.
(c)
Answer to Problem 37PPS
About 20,654 people owned digital audio player last year.
Explanation of Solution
Given information:
From the stable population of 25,000 people,
17,252 own digital audio players and 7748 own portable CD players.
Calculation:
Calculate the inverse of a
Substitute the values:
Now,
Obtain the identity matrix by multiplying original with inverse:
Then
Use the inverse matrix to obtain the matrix equation.
Perform the multiplication:
Simplify:
That becomes
Therefore,
About 20,654 people owned digital audio player last year.
Chapter 3 Solutions
Glencoe Algebra 2 Student Edition C2014
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