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Matrix for word problem

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Four theaters comprise the Cinema Center: Cinemas I, II, III, and IV. The admission price for one feature at the Center is $2 for children, $3.50 for students, and $5.75 for adults. Suppose that on a particular Sunday 240 children, 100 students, and 75 adults attended the evening show in Cinema I; 60 children, 240 students, and 290 adults attended the evening show in Cinema II. 300 children, 63 students, and 107 adults attended the evening show in Cinema III. No children, 197 students, and 183 adults attended the evening show at Cinema IV.

Write a matrix A that represents the Cinemas, and the number of each type (children, student, or adult) that attended each Cinema.

Write a column vector B representing admission prices.

Perform the multiplication AB and explain what this product represents.

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Solution Summary

This provides an example of using a matrix to solve a word problem.

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Matrix Word Problem

Please answer the following Matrix Word Problem, and number 10, 22, and 30. Please show all your work in steps.

When two kittens named Cauchy and Cliché were introduced into a household with Jamie (an older cat) and Musk (a dog), the interactions between animals were complicated. The two kittens liked each other and Jamie, but didn't like Musk. Musk liked everybody, but Jamie didn't like any of the other animals.

a. Write a matrix in which rows (and columns) 1, 2, 3, and 4 refer to Musk, Jamie, Cauchy, and Cliché. Make an element a 1 if the animal for that row likes the animal for that column, and otherwise make the element a 0. Assume every animal likes herself.

b.Within a few days, Cauchy and Cliché decided that they liked Musk after all. Write a matrix, as you did in part a, representing the new situation.

Please see the attached for the problems.

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