Use matrices to solve the problem

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In summary, the problem is about using matrices to solve the distribution of market share among three major soda companies (Coca-Cola, Pepsi, and 7up) over the course of one year and ten years. The given data shows that after one year, Coke has 25% of the market, Pepsi has 33%, and 7up has 18%. However, these percentages do not add up to 100%, indicating a mistake in the calculation. The original amount of soda pop drinkers for each company is unknown, but it can be calculated using the given data and cramer's rule. It is not clear if 7up will ever lose all of its market, but further information or analysis is needed to justify an answer.
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josh_123
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Here is the problem:

Use matrices to solve the following problems:Show your matrices that you use as well as your solutions.

Classroom Example: The three major companies are coca cola, pepsi and 7up. Coca-Cola has a 40% share of the soda market, Pepsi has 40% of the soda market and 7up has the remaining 20% of the soda market. Each year, Coke retains 80% of its market, but loses 15% to pepsi and 5% to 7 up. The Pepsi company retains 90% of its market, but loses 5% to coke and 5% to 7up. The 7 up company retains 70% of its market, but loses 20% to Coke and 10% to Pepsi. After one year, what percentage of the total soda market does each company have?

After 10 years, what is the percentage of the total soda market, does each company have?

If the total soda market is 3.5 million people, what is the amount of soda pop drinkers for each company originally?After one year?After 10 years?

Will 7up ever lose all of its market?Justify your answer.


I've try using the cramer's rule and set it up like this:

[.80 -.15 -.05
.90 -.05 -.05
.70 -.20 -.10] this is a 3x3

multiply by
[.40
.40
.20] and this is a 3x1 so the answer will be a 3x1

[.25
.33
.18]

then multiply it by a 100 to get all the percent. I got 25% for Coke, 33% for Pepsi and 18% for 7up. I think this is wrong because when you add up the three percent up it not end up to be a 100%. Are there any way I can get this one right?please help and thank you
 
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hi is anyone have an answer?I really need help
 

1. How do matrices help in solving problems?

Matrices are a mathematical tool that can help represent and manipulate data in a structured way. By using matrices, we can perform operations such as addition, subtraction, multiplication, and division on a set of numbers or variables.

2. What types of problems can be solved using matrices?

Matrices can be used to solve a variety of problems in different fields such as engineering, physics, economics, and computer science. Some common examples include linear equations, systems of equations, transformations, and optimization problems.

3. Can matrices be used to solve real-world problems?

Yes, matrices can be used to solve real-world problems that involve large amounts of data and complex calculations. For example, matrices are commonly used in data analysis, image processing, and machine learning algorithms.

4. How do you perform matrix operations to solve a problem?

To solve a problem using matrices, we need to use certain rules and methods to perform operations such as addition, subtraction, multiplication, and division. These operations involve manipulating the elements of the matrices according to specific rules to obtain the desired solution.

5. Are there any limitations to using matrices to solve problems?

While matrices are a powerful tool for solving problems, they do have some limitations. For example, not all problems can be represented in matrix form, and some problems may require advanced techniques or specialized software to be solved using matrices.

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