Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
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Chapter 3.7, Problem 32EQ
To determine

Given a consumption matrix C and a demand vector d,C = [0.10.40.30.2] and d = [21]To find the feasible production vector x.

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Consider the basic macroeconomic model: Y=C+I and C = a + by where Y is GDP, C is consumtion and I is total investment (treated as fixed). a, b are positive parameters. Solve the model for Y in terms of I and the parameters.
Q-1 A manufacturer of microcomputers produces three different models. The following table summarizes whole sale process material cost per unit, and labor cost per unit. The annual fixed cost is Rs. 10 Million. But manufacturer decided that fifty percent more annual costs would be include in its sanarios and the fixed cost 4400, 8000 and 3500 are also included each of three models. Product Туре 1 Туре 2 Туре 3 Whole Sale Price/ Unit Rs. 950 1000 1500 Material Cost/Unit 200 300 230 Labor Cost/Unit 175 150 450 Required: i) Determine a joint total revenue function for the sales of the three different microcomputer models. ii) iii) iv) Determine a total cost function for manufacturing the three models. Determine the profit function for sale of the three models. What is annual profit, if the firm sells 60,000, 13000 and units of three models? 100400 v) Also graphically present all functions.
SECTIONS 1.4, 5.5 - Use the following equations to answer the questions. Demand Function: p = D(x) = (x - 7)², Supply Function: p = S(x) = x + 2x + 1 %3D a. Find the equilibrium point (xo , Po ).Write as an ordered pair. b. Use calculus to find the consumer surplus at the equilibrium point found in the last question. Write an exact answer. State the formula for consumer surplus. (Note: If you were unable to find the equilibrium point, use (8, 1) for this question.) Formula: Consumer Surplus =, c. Use calculus to find the producer surplus at the equilibrium point found in the second to last question. Write an exact answer. State the formula for consumer surplus. (Note: If you were unable to find the equilibrium point, use (2, 5) for this question.) Formula: Producer Surplus =

Chapter 3 Solutions

Linear Algebra: A Modern Introduction

Ch. 3.1 - Let In Exercises 1-16, compute the indicated...Ch. 3.1 - Let In Exercises 1-16, compute the indicated...Ch. 3.1 - Let...Ch. 3.1 - Let...Ch. 3.1 - Let...Ch. 3.1 - Let...Ch. 3.1 - Give an example of a nonzero 22 matrix A such that...Ch. 3.1 - Let A=[2613]. Find 22 matrices B and C such that...Ch. 3.1 - A factory manufactures three products (doohickies,...Ch. 3.1 - Referring to Exercise 19, suppose that the unit...Ch. 3.1 - In Exercises 21-22, write the given system of...Ch. 3.1 - In Exercises 21-22, write the given system of...Ch. 3.1 - In Exercises 23-28, let A=[102311201] and...Ch. 3.1 - In Exercises 23-28, let and 24. Use the...Ch. 3.1 - In Exercises 23-28, let and 25. Compute the...Ch. 3.1 - In Exercises 23-28, let A=[102311201] and...Ch. 3.1 - In Exercises 23-28, let and 27. Use the...Ch. 3.1 - Prob. 28EQCh. 3.1 - In Exercises 29 and 30, assume that the product AB...Ch. 3.1 - Prob. 30EQCh. 3.1 - In Exercises 31-34, compute AB by block...Ch. 3.1 - In Exercises 31-34, compute AB by block...Ch. 3.1 - In Exercises 31-34, compute AB by block...Ch. 3.1 - In Exercises 31-34, compute AB by block...Ch. 3.1 - Prob. 35EQCh. 3.1 - Let B=[12121212]. Find, with justification, B2015.Ch. 3.1 - Let A=[1101]. Find a formula for An(n1) and verify...Ch. 3.1 - 38. Let (a) Show that (b) Prove, by mathematical...Ch. 3.1 - In each of the following, find the 66matrixA=[aij]...Ch. 3.2 - In Exercises 1-4, solve the equation for X, given...Ch. 3.2 - In Exercises 1-4, solve the equation for X, given...Ch. 3.2 - In Exercises 1-4, solve the equation for X, given...Ch. 3.2 - In Exercises 1-4, solve the equation for X, given...Ch. 3.2 - In Exercises 5-8, write B as a linear combination...Ch. 3.2 - In Exercises 5-8, write B as a linear combination...Ch. 3.2 - In Exercises 5-8, write B as a linear combination...Ch. 3.2 - In Exercises 5-8, write B as a linear combination...Ch. 3.2 - In Exercises 9-12, find the general form of the...Ch. 3.2 - In Exercises 9-12, find the general form of the...Ch. 3.2 - In Exercises 9-12, find the general form of the...Ch. 3.2 - In Exercises 9-12, find the general form of the...Ch. 3.2 - In Exercises 13-16, determine whether the given...Ch. 3.2 - In Exercises 13-16, determine whether the given...Ch. 3.2 - In Exercises 13-16, determine whether the given...Ch. 3.2 - In Exercises 13-16, determine whether the given...Ch. 3.2 - 17. Prove Theorem 3.2(a) -(d).Ch. 3.2 - Prove Theorem 3.2 (e) (h).Ch. 3.2 - Prove Theorem 3.3(c).Ch. 3.2 - Prove Theorem 3.3(d).Ch. 3.2 - Prove the half of Theorem 3.3 (e) that was not...Ch. 3.2 - 22. Prove that, for square matrices A and B, AB =...Ch. 3.2 - In Exercises 23-25, if , find conditions on a, b,...Ch. 3.2 - In Exercises 23-25, if B=[abcd], find conditions...Ch. 3.2 - In Exercises 23-25, B=[abcd], find conditions on...Ch. 3.2 - 26. Find conditions on a, b, c, and d such that ...Ch. 3.2 - 27. Find conditions on a, b, c, and d such that ...Ch. 3.2 - Prove that if AB and BA are both defined, then AB...Ch. 3.2 - A square matrix is called upper triangular if all...Ch. 3.2 - 33. Using induction, prove that for all . Ch. 3.3 - In Exercises 1-10, find the inverse of the given...Ch. 3.3 - In Exercises 1-10, find the inverse of the given...Ch. 3.3 - In Exercises 1-10, find the inverse of the given...Ch. 3.3 - In Exercises 1-10, find the inverse of the given...Ch. 3.3 - In Exercises 5-8, write B as a linear combination...Ch. 3.3 - Prob. 6EQCh. 3.3 - In Exercises 1-10, find the inverse of the given...Ch. 3.3 - In Exercises 1-10, find the inverse of the given...Ch. 3.3 - In Exercises 1-10, find the inverse of the given...Ch. 3.3 - In Exercises 1-10, find the inverse of the given...Ch. 3.3 - In Exercises 11 and 12, solve the given system...Ch. 3.3 - In Exercises 11 and 12, solve the given system...Ch. 3.3 - Let A=[1226],b1=[35],b2=[12],andb3=[20]. Find A-1...Ch. 3.3 - In Exercises 20-23, solve the given matrix...Ch. 3.3 - In Exercises 20-23, solve the given matrix...Ch. 3.3 - In Exercises 20-23, solve the given matrix...Ch. 3.3 - In Exercises 20-23, solve the given matrix...Ch. 3.3 - In Exercises let In each case, find an...Ch. 3.3 - Prob. 25EQCh. 3.3 - Prob. 26EQCh. 3.3 - Prob. 27EQCh. 3.3 - Prob. 28EQCh. 3.3 - Prob. 29EQCh. 3.3 - Prob. 30EQCh. 3.3 - Prob. 31EQCh. 3.3 - Prob. 32EQCh. 3.3 - In Exercises 31-38, find the inverse of the given...Ch. 3.3 - In Exercises 31-38, find the inverse of the given...Ch. 3.3 - In Exercises 31-38, find the inverse of the given...Ch. 3.3 - In Exercises 31-38, find the inverse of the given...Ch. 3.3 - Prob. 48EQCh. 3.3 - Prob. 49EQCh. 3.3 - In Exercises 48-63, use the Gauss-Jordan method to...Ch. 3.3 - Prob. 51EQCh. 3.3 - In Exercises 48-63, use the Gauss-Jordan method to...Ch. 3.3 - In Exercises 48-63, use the Gauss-Jordan method to...Ch. 3.3 - Prob. 54EQCh. 3.3 - Prob. 55EQCh. 3.3 - In Exercises 48-63, use the Gauss-Jordan method to...Ch. 3.3 - In Exercises 48-63, use the Gauss-Jordan method to...Ch. 3.3 - Prob. 60EQCh. 3.3 - Prob. 61EQCh. 3.3 - In Exercises 48-63, use the Gauss-Jordan method to...Ch. 3.3 - In Exercises 48-63, use the Gauss-Jordan method to...Ch. 3.4 - In Exercises 1 -6, solve the system Ax = b using...Ch. 3.4 - In Exercises 1 6, solve the system Ax = b using...Ch. 3.4 - In Exercises 1 -6, solve the system Ax = b using...Ch. 3.4 - In Exercises 1 -6, solve the system Ax = b using...Ch. 3.4 - In Exercises 1-6, solve the system Ax = b using...Ch. 3.4 - Prob. 6EQCh. 3.4 - In Exercises 7-12, find an LU factorization of the...Ch. 3.4 - In Exercises 7-12,find an LU factorization of the...Ch. 3.4 - In Exercises 7-12, find an LU factorization of the...Ch. 3.4 - In Exercises 7-12,find an LU factorization of the...Ch. 3.4 - In Exercises 7-12,find an LU factorization of the...Ch. 3.4 - Prob. 12EQCh. 3.4 - Generalize the definition of LU factorization to...Ch. 3.4 - Prob. 14EQCh. 3.5 - In Exercises 1-4, let S be the collection of...Ch. 3.5 - In Exercises 5-8, let S be the collection of...Ch. 3.5 - In Exercises 11 and 12, determine whether b is in...Ch. 3.5 - If A is the matrix in Exercise 12, is v=[712] in...Ch. 3.6 - 1. Let Ta : ℝ2 → ℝ2 be the matrix transformation...Ch. 3.6 - Let TA: 23 be the matrix transformation...Ch. 3.6 - In Exercises 3-6, prove that the given...Ch. 3.6 - In Exercises 3-6, prove that the given...Ch. 3.6 - Prob. 5EQCh. 3.6 - In Exercises 3-6, prove that the given...Ch. 3.6 - In Exercises 7-10, give a counterexample to show...Ch. 3.6 - In Exercises 7-10, give a counterexample to show...Ch. 3.6 - In Exercises 7-10, give a counterexample to show...Ch. 3.6 - In Exercises 7-10, give a counterexample to show...Ch. 3.6 - In Exercises 11-14, find the standard matrix of...Ch. 3.6 - In Exercises 11-14, find the standard matrix of...Ch. 3.6 - In Exercises 11-14, find the standard matrix of...Ch. 3.6 - In Exercises 11-14, find the standard matrix of...Ch. 3.6 - In Exercises 15-18, show that the given...Ch. 3.6 - In Exercises 15-18, show that the given...Ch. 3.6 - Prob. 17EQCh. 3.6 - Prob. 18EQCh. 3.6 - In Exercises 20-25, find the standard matrix of...Ch. 3.6 - In Exercises 20-25, find the standard matrix of...Ch. 3.6 - In Exercises 20-25, find the standard matrix of...Ch. 3.6 - In Exercises 20-25, find the standard matrix of...Ch. 3.6 - In Exercises 20-25, find the standard matrix of...Ch. 3.6 - In Exercises 20-25, find the standard matrix of...Ch. 3.6 - In Exercises30-35, verify Theorem 3.32 by finding...Ch. 3.6 - In Exercises 30-35, verify Theorem 3.32 by finding...Ch. 3.6 - In Exercises 30-35, verify Theorem 3.32 by finding...Ch. 3.6 - In Exercises 30-35, verify Theorem 3.32 by finding...Ch. 3.6 - In Exercises30-35, verify Theorem 3.32 by finding...Ch. 3.6 - Prob. 35EQCh. 3.7 - In Exercises 1-4, let be the transition matrix...Ch. 3.7 - Prob. 2EQCh. 3.7 - In Exercises 1-4, let P=[0.50.30.50.7] be the...Ch. 3.7 - In Exercises 1-4, let be the transition matrix for...Ch. 3.7 - Prob. 5EQCh. 3.7 - Prob. 6EQCh. 3.7 - Prob. 7EQCh. 3.7 - Prob. 8EQCh. 3.7 - 12. Robots have been programmed to traverse the...Ch. 3.7 - Prob. 31EQCh. 3.7 - Prob. 32EQCh. 3.7 - Prob. 33EQCh. 3.7 - Prob. 34EQCh. 3.7 - Prob. 35EQCh. 3.7 - Prob. 36EQCh. 3.7 - Prob. 37EQCh. 3.7 - Prob. 38EQCh. 3.7 - Prob. 39EQCh. 3.7 - Prob. 40EQCh. 3.7 - In Exercises 45-48, determine the adjacency matrix...Ch. 3.7 - Prob. 46EQCh. 3.7 - In Exercises 45-48, determine the adjacency matrix...Ch. 3.7 - In Exercises 45-48, determine the adjacency matrix...Ch. 3.7 - Prob. 53EQCh. 3.7 - In Exercises 53-56, determine the adjacency matrix...Ch. 3.7 - In Exercises 53-56, determine the adjacency matrix...Ch. 3.7 - In Exercises 53-56, determine the adjacency matrix...
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