Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
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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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The augmented matrix of a linear system has been reduced by row operations to the
form shown. Continue the appropriate row operations and describe the solution set of the
original system.
1 -1
0 1 -2
00-4
0-6
0
0
1
- 3
3
0
001
4
Solve the system.
X1
-
3x3
=
10
4x1
+ 2x2 + 3x3 =
22
×2 + 4x3
=
-2
Use the quadratic formula to find the zeros of the quadratic equation.
Y=3x^2+48x+180
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. 11EQCh. 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. 30EQCh. 2.1 - In Exercises 31 and 32, find a system of linear...Ch. 2.1 - Prob. 32EQCh. 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. 17EQCh. 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. 24EQCh. 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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