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Math Algebra Linear Algebra: A Modern Introduction

Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.

Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.

Solution Summary: The author explains the relative outputs of farming and manufacturing industries. Farming consumes 1/2 food and 1/3 of manufactured goods.

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN: 9781285463247

Author: David Poole

Publisher: Cengage Learning

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Textbook Question

Chapter 2.4, Problem 23EQ

Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.

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Chapter 2.4, Problem 22EQ

Chapter 2.4, Problem 24EQ

Chapter 2 Solutions

Linear Algebra: A Modern Introduction

Ch. 2.1 - In Exercises 1-6, determine which equations are...Ch. 2.1 - In Exercises 1-6, determine which equations are...Ch. 2.1 - In Exercises 1-6, determine which equations are...Ch. 2.1 - In Exercises 1-6, determine which equations are...Ch. 2.1 - In Exercises 1-6, determine which equations are...Ch. 2.1 - In Exercises 1-6, determine which equations are...Ch. 2.1 - In Exercises 7-10, find a linear equation that has...Ch. 2.1 - In Exercises 7-10, find a linear equation that has...Ch. 2.1 - In Exercises 7-10, find a linear equation that has...Ch. 2.1 - In Exercises 7-10, find a linear equation that has...

Ch. 2.1 - Prob. 11EQ Ch. 2.1 - In Exercises 11-14, find the solution set of each...Ch. 2.1 - In Exercises 11-14, find the solution set of each...Ch. 2.1 - In Exercises 11-14, find the solution set of each...Ch. 2.1 - In Exercises 19-24, solve the given system by back...Ch. 2.1 - In Exercises 19-24, solve the given system by back...Ch. 2.1 - In Exercises 19-24, solve the given system by back...Ch. 2.1 - In Exercises 19-24, solve the given system by back...Ch. 2.1 - In Exercises 19-24, solve the given system by back...Ch. 2.1 - In Exercises 19-24, solve the given system by back...Ch. 2.1 - The systems in Exercises 25 and 26 exhibit a lower...Ch. 2.1 - The systems in Exercises 25 and 26 exhibit a lower...Ch. 2.1 - Find the augmented matrices of the linear systems...Ch. 2.1 - Find the augmented matrices of the linear systems...Ch. 2.1 - Find the augmented matrices of the linear systems...Ch. 2.1 - Prob. 30EQ Ch. 2.1 - In Exercises 31 and 32, find a system of linear...Ch. 2.1 - Prob. 32EQ Ch. 2.2 - In Exercises 1-8, determine whether the given...Ch. 2.2 - In Exercises 1-8, determine whether the given...Ch. 2.2 - In Exercises 1-8, determine whether the given...Ch. 2.2 - In Exercises 1-8, determine whether the given...Ch. 2.2 - In Exercises 1-8, determine whether the given...Ch. 2.2 - In Exercises 1-8, determine whether the given...Ch. 2.2 - In Exercises 1-8, determine whether the given...Ch. 2.2 - In Exercises 1-8, determine whether the given...Ch. 2.2 - In Exercises 9-14, use elementary row operations...Ch. 2.2 - In Exercises 9-14, use elementary row operations...Ch. 2.2 - In Exercises 9-14, use elementary row operations...Ch. 2.2 - In Exercises 9-14, use elementary row operations...Ch. 2.2 - In Exercises 9-14, use elementary row operations...Ch. 2.2 - In Exercises 9-14, use elementary row operations...Ch. 2.2 - 15. Reverse the elementary row operations used in...Ch. 2.2 - 16. In general, what is the elementary row...Ch. 2.2 - Prob. 17EQ Ch. 2.2 - In Exercises 17 and 18, show that the given...Ch. 2.2 - 19. What is wrong with the following “proof” that...Ch. 2.2 - What is the net effect of performing the following...Ch. 2.2 - Students frequently perform the following type of...Ch. 2.2 - Consider the matrix A=[2314]. Show that any of the...Ch. 2.2 - What is the rank of each of the matrices in...Ch. 2.2 - Prob. 24EQ Ch. 2.2 - In Exercises 25-34, solve the given system of...Ch. 2.2 - In Exercises 25-34, solve the given system of...Ch. 2.2 - In Exercises 25-34, solve the given system of...Ch. 2.2 - In Exercises 25-34, solve the given system of...Ch. 2.2 - In Exercises 25-34, solve the given system of...Ch. 2.2 - In Exercises 25-34, solve the given system of...Ch. 2.2 - In Exercises 25-34, solve the given system of...Ch. 2.3 - In Exercises 1-6, determine if the vector is a...Ch. 2.3 - In Exercises 1-6, determine if the vector is a...Ch. 2.3 - In Exercises 1-6, determine if the vector is a...Ch. 2.3 - In Exercises 1-6, determine if the vector vis a...Ch. 2.3 - In Exercises 1-6, determine if the vector is a...Ch. 2.3 - In Exercises 7 and 8, determine if the vector b is...Ch. 2.3 - Show that 3=span([101],[110],[011])Ch. 2.3 - Use the method of Example 2.23 and Theorem 2.6 to...Ch. 2.3 - Use the method of Example 2.23 and Theorem 2.6 to...Ch. 2.3 - Use the method of Example 2.23 and Theorem 2.6 to...Ch. 2.4 - 1. Suppose that, in Example 2.27, 400 units of...Ch. 2.4 - 2. Suppose that in Example 2.27, 400 units of food...Ch. 2.4 - A florist offers three sizes of flower...Ch. 2.4 - 4. (a) In your pocket you have some nickels,...Ch. 2.4 - 5. A coffee merchant sells three blends of coffee....Ch. 2.4 - Redo Exercise 5, assuming that the house blend...Ch. 2.4 - In Exercises 7-14, balance the chemical equation...Ch. 2.4 - In Exercises 7-14, balance the chemical equation...Ch. 2.4 - In Exercises 7-14, balance the chemical equation...Ch. 2.4 - In Exercises 7-14, balance the chemical equation...Ch. 2.4 - In Exercises 7-14, balance the chemical equation...Ch. 2.4 - In Exercises 7-14, balance the chemical equation...Ch. 2.4 - In Exercises 7-14, balance the chemical equation...Ch. 2.4 - In Exercises 7-14, balance the chemical equation...Ch. 2.4 - For Exercises 19 and 20, determine the currents...Ch. 2.4 - For Exercises 19 and 20, determine the currents...Ch. 2.4 - 21. (a) Find the currents in the bridge circuit...Ch. 2.4 - 22. The networks in parts (a) and (b) of Figure...Ch. 2.4 - 23. Consider a simple economy with just two...Ch. 2.4 - Suppose the coal and steel industries form a...Ch. 2.4 - 25. A painter, a plumber, and an electrician...Ch. 2.4 - 31. In Example 2.35, describe all possible...Ch. 2 - What is the maximum rank of a 53 matrix? What is...

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Redo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of Kenyan beans, and 150 grams of French roast beans and the gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyan beans, and 50 grams of French roast beans. This time the merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 15 kilograms of French roast beans. Suppose one bag of the house blend produces a profit of $0.50, one bag of the special blend produces a profit of $1.50, and one bag of the gourmet blend produces a profit of $2.00. How many bags of each type should the merchant prepare if he wants to use up all of the beans and maximize his profit? What is the maximum profit?

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