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22. Models of markets. Determine the equilibrium solution (D₁ = S₁, D2 = S₂) of the two-commodity market with linear model (D, S, P = demand, supply, price; index 1 = first commodity, index 2 = second commodity) D₁402P₁ - P₂, D₂ = 5P₁ - 2P₂ + 16, S₁ = 4P₁ P₂ + 4, S₂ = 3P₂ - 4.

22. Models of markets. Determine the equilibrium solution (D₁ = S₁, D2 = S₂) of the two-commodity market with linear model (D, S, P = demand, supply, price; index 1 = first commodity, index 2 = second commodity) D₁402P₁ - P₂, D₂ = 5P₁ - 2P₂ + 16, S₁ = 4P₁ P₂ + 4, S₂ = 3P₂ - 4.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
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Number 22

17-21 MODELS OF NETWORKS In Probs. 17-19, using Kirchhoff's laws (see Example 2) and showing the details, find the currents: 17. 16 V 18. to Probs. 11-14 and to some larger systems of your choice. 19. 292 1₁ 4Ω 4Ω 12 V EV₁ W 192 32 V 292 13 11 √1₂ 1292 1₂ R₁ Q 24 V 1₂ 13 892 R₂ www 20. Wheatstone bridge. Show that if Rx/R3 = R₁/R₂ in 22. Models of markets. Determine the equilibrium solution (D₁ = S₁, D2 = S₂) of the two-commodity market with linear model (D, S, P = demand, supply, price; index 1 = first commodity, index 2 = second commodity) D₁ = 402P₁ - P2, D₂ = 5P₁ - 2P₂ + 16, 23. Balancing a chemical equation x₁C3H8 + x20₂- x3CO₂ + x4H₂O means finding integer X1, X2, X3, X4 such that the numbers of atoms of carbon (C), hydrogen (H), and oxygen (O) are the same on both sides of this reaction, in which propane C3H8 and O₂ give carbon dioxide and water. Find the smallest positive integers X1,***, X4. S₁ = 4P₁ P₂ + 4, S₂ = 3P₂ - 4. 24. PROJECT. Elementary Matrices. The idea is that elementary operations can be accomplished by matrix multiplication. If A is an m X n matrix on which we want to do an elementary operation, then there is a matrix E such that EA is the new matrix after the operation. Such an E is called an elementary matrix. This idea can be helpful, for instance, in the design of algorithms. (Computationally, it is generally prefer- able to do row operations directly, rather than by multiplication by E.) (a) Show that the following are elementary matrices, for interchanging Rows 2 and 3, for adding -5 times the first row to the third, and for multiplying the fourth
Transcribed Image Text:17-21 MODELS OF NETWORKS In Probs. 17-19, using Kirchhoff's laws (see Example 2) and showing the details, find the currents: 17. 16 V 18. to Probs. 11-14 and to some larger systems of your choice. 19. 292 1₁ 4Ω 4Ω 12 V EV₁ W 192 32 V 292 13 11 √1₂ 1292 1₂ R₁ Q 24 V 1₂ 13 892 R₂ www 20. Wheatstone bridge. Show that if Rx/R3 = R₁/R₂ in 22. Models of markets. Determine the equilibrium solution (D₁ = S₁, D2 = S₂) of the two-commodity market with linear model (D, S, P = demand, supply, price; index 1 = first commodity, index 2 = second commodity) D₁ = 402P₁ - P2, D₂ = 5P₁ - 2P₂ + 16, 23. Balancing a chemical equation x₁C3H8 + x20₂- x3CO₂ + x4H₂O means finding integer X1, X2, X3, X4 such that the numbers of atoms of carbon (C), hydrogen (H), and oxygen (O) are the same on both sides of this reaction, in which propane C3H8 and O₂ give carbon dioxide and water. Find the smallest positive integers X1,***, X4. S₁ = 4P₁ P₂ + 4, S₂ = 3P₂ - 4. 24. PROJECT. Elementary Matrices. The idea is that elementary operations can be accomplished by matrix multiplication. If A is an m X n matrix on which we want to do an elementary operation, then there is a matrix E such that EA is the new matrix after the operation. Such an E is called an elementary matrix. This idea can be helpful, for instance, in the design of algorithms. (Computationally, it is generally prefer- able to do row operations directly, rather than by multiplication by E.) (a) Show that the following are elementary matrices, for interchanging Rows 2 and 3, for adding -5 times the first row to the third, and for multiplying the fourth
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