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mathematics
mathematical applications for the management

Questions and Answers of Mathematical Applications for the Management

Use the matrices below as needed to complete Problems.Perform the indicated operations in ProblemsA + B 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 | I
Which three industries would be most affected by a rise in the cost of raw materials?The following technology matrix describes the relationship of certain industries within the economy to each other.
If AX = B andfind the matrix X. 1 A- 3 1 2 and B = 1 4 1 1 3. ||
In Problems, find the inverse matrix for each matrix that has an inverse. 4 7 2 1
In Problem use matrices A through F. In Problem, perform the indicated operations when possible.AB 1 2 1 1 A = 3 1 B = | 4 2 1 4 0 3 3 1 D=: 3 4 2 C = 1 5 1 E = 4 0. -1 3 F = 1 -1 -4 3. 3. 1. 3.
In Problem an augmented matrix for a system of linear equations in x, y, and z is given. Find the solution of each system. 1 5 -4 2 -2 4 -2 1 -3 7] 2.
Use the matrices below as needed to complete Problems.Perform the indicated operations in ProblemsC - E 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 | I
What is element b24?Use the following matrices 1 -2 1 A = 1 B =| 4 1 2 0 1 c- --] -- : 3 4 D = 3 1 E = 5 4 C 1 1. 3 2 1 1 F = -1 1 G = 1 4 3 -4 5 1 Z = 3. 1. 3. 3. 4,
Which industry would be most affected by a rise in the cost of manufactured goods?The following technology matrix describes the relationship of certain industries within the economy to each other.
Solve х — у+ 223D 4 X - x + 4y + z = 4 2х + 2y + 4z %3D 10
In Problems, find the inverse matrix for each matrix that has an inverse. [: 6. -4 -1 1
In Problems 5–24, use matrices A through F. In Problems perform the indicated operations when possible.EC A = 1 0 2 3 2 1 4 0 3 5 3 c-[] C 2 E = 1 0 4 5 1 0 B = D= F = 4 3 4. 3 1 2 13 0 1 1 2 2 ] 2
In Problem an augmented matrix for a system of linear equations in x, y, and z is given. Find the solution of each system. -2 4 1 4 2. 3.
Use the matrices below as needed to complete Problems.Perform the indicated operations in ProblemsDT - I 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 |
Write the transpose of matrix A.Use the following matrices 1 -2 1 A = 1 B =| 4 1 2 0 1 c- --] -- : 3 4 D = 3 1 E = 5 4 C 1 1. 3 2 1 1 F = -1 1 G = 1 4 3 -4 5 1 Z = 3. 1. 3. 3. 4,
Solve х — у +223D 4 x + 4y + z = 4 2х + 3у + 3z%3D 8
In Problem use matrices A through F. In Problem, perform the indicated operations when possible.BA 1 2 1 1 A = 3 1 B = | 4 2 1 4 0 3 3 1 D=: 3 4 2 C = 1 5 1 E = 4 0. -1 3 F = 1 -1 -4 3. 3. 1. 3.
Use the matrices below as needed to complete Problems.Perform the indicated operations in Problems3C 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 | I =
Write the transpose of matrix F.Use the following matrices 1 -2 1 A = 1 B =| 4 1 2 0 1 c- --] -- : 3 4 D = 3 1 E = 5 4 C 1 1. 3 2 1 1 F = -1 1 G = 1 4 3 -4 5 1 Z = 3. 1. 3. 3. 4,
Solve х — у+323D 4 y = 4 х+ 5у + 2z %3D3 2х + 4у + 5z 3D 8
In Problem use matrices A through F. In Problem, perform the indicated operations when possible.FBT 1 2 1 1 A = 3 1 B = | 4 2 1 4 0 3 3 1 D=: 3 4 2 C = 1 5 1 E = 4 0. -1 3 F = 1 -1 -4 3. 3. 1. 3.
Use the matrices below as needed to complete Problems.Perform the indicated operations in Problems4I 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 | I =
What is the sum of matrix A and its negative?Use the following matrices 1 -2 1 A = 1 B =| 4 1 2 0 1 c- --] -- : 3 4 D = 3 1 E = 5 4 C 1 1. 3 2 1 1 F = -1 1 G = 1 4 3 -4 5 1 Z = 3. 1. 3. 3. 4,
Use an inverse matrix to solve x + y + 2z 4 х + 2у + z+ w3D 4 z + w = 4 2х + 5у + 4z+ 2w 3D 10 2у + z+ 2w 3 0
In Problem use matrices A through F. In Problem, perform the indicated operations when possible.EB 1 2 1 1 A = 3 1 B = | 4 2 1 4 0 3 3 1 D=: 3 4 2 C = 1 5 1 E = 4 0. -1 3 F = 1 -1 -4 3. 3. 1. 3.
Use the matrices below as needed to complete Problems.Perform the indicated operations in Problems-2F 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 | I =
If matrix A has element a3j = 0, what is j?Use the following matrices 1 -2 1 A = 1 B =| 4 1 2 0 1 c- --] -- : 3 4 D = 3 1 E = 5 4 C 1 1. 3 2 1 1 F = -1 1 G = 1 4 3 -4 5 1 Z = 3. 1. 3. 3. 4,
In Problems, graph each inequality.y ≤ 2x - 1
Solve x - y + 2z - w = 4 x + 4y + z + w = 4 2x + 2y + 4z + 2w = 10 y + z + 2w =
In Problem use matrices A through F. In Problem, perform the indicated operations when possible.BE 1 2 1 1 A = 3 1 B = | 4 2 1 4 0 3 3 1 D=: 3 4 2 C = 1 5 1 E = 4 0. -1 3 F = 1 -1 -4 3. 3. 1. 3.
Use the matrices below as needed to complete Problems.Perform the indicated operations in Problems4D - 3I 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 |
Suppose that the solution of an investment problem involving a system of linear equations is given byB = 75,000 - 3H and E = 20,000 + 2Hwhere B represents the dollars invested in Barton Bank stocks,
In Problem use matrices A through F. In Problem, perform the indicated operations when possible.EAT 1 2 1 1 A = 3 1 B = | 4 2 1 4 0 3 3 1 D=: 3 4 2 C = 1 5 1 E = 4 0. -1 3 F = 1 -1 -4 3. 3. 1. 3.
In Problem use row operations on augmented matrices to solve the given systems of linear equations. x - 2y + 3z + w = -2 x - 3y + z - w = -7 y = -2 + z + w = 2.
Use the matrices below as needed to complete Problems.Perform the indicated operations in ProblemsF + 2D 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 |
In an ecological model, matrix A gives the fractions of several types of plants consumed by the herbivores in the ecosystem. Similarly, matrix B gives the fraction of each type of herbivore that is
In Problem use matrices A through F. In Problem, perform the indicated operations when possible.AET 1 2 1 1 A = 3 1 B = | 4 2 1 4 0 3 3 1 D=: 3 4 2 C = 1 5 1 E = 4 0. -1 3 F = 1 -1 -4 3. 3. 1. 3.
In Problem use row operations on augmented matrices to solve the given systems of linear equations. x + 4y – 6z – 3w = 3 x - y + 2w = -5 + z + w = 1. y + z + w =
A furniture manufacturer produces four styles of chairs and has orders for 1000 of style A, 4000 of style B, 2000 of style C, and 1000 of style D. The following table lists the numbers of units of
In Problem use matrices A through F. In Problem, perform the indicated operations when possible.A2 1 2 1 1 A = 3 1 B = | 4 2 1 4 0 3 3 1 D=: 3 4 2 C = 1 5 1 E = 4 0. -1 3 F = 1 -1 -4 3. 3. 1. 3.
Use the matrices below as needed to complete Problems.Perform the indicated operations in ProblemsAC 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 | I =
In Problem perform the operations if possible.Z + GT
Complete parts (a) and (b) using the code discussed in Sections 3.2 and 3.4 (where a is 1, . . . , z is 26, and blank is 27), and the coding matrix is(a) Encode the message “Less is more,” the
In Problem use matrices A through F. In Problem, perform the indicated operations when possible.A3 1 2 1 1 A = 3 1 B = | 4 2 1 4 0 3 3 1 D=: 3 4 2 C = 1 5 1 E = 4 0. -1 3 F = 1 -1 -4 3. 3. 1. 3.
Use the matrices below as needed to complete Problems.Perform the indicated operations in ProblemsCD 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 | I =
In Problem perform the operations if possible.A + AT
A young couple with a $120,000 inheritance wants to invest all this money. They plan to diversify their investments, choosing some of each of the following types of stock.Their strategy is to have
In Problem use matrices A through F. In Problem, perform the indicated operations when possible.C3 1 2 1 1 A = 3 1 B = | 4 2 1 4 0 3 3 1 D=: 3 4 2 C = 1 5 1 E = 4 0. -1 3 F = 1 -1 -4 3. 3. 1. 3.
Use the matrices below as needed to complete Problems.Perform the indicated operations in ProblemsDF 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 | I =
In Problem perform the operations if possible.A + FT
Suppose an economy has two industries, agriculture and minerals, and the economy has the technology matrix(a) If surpluses of 100 agriculture units and 140 minerals units are desired, find the gross
In Problem use matrices A through F. In Problem, perform the indicated operations when possible.F2 1 2 1 1 A = 3 1 B = | 4 2 1 4 0 3 3 1 D=: 3 4 2 C = 1 5 1 E = 4 0. -1 3 F = 1 -1 -4 3. 3. 1. 3.
In Problems, find the inverse matrix for each matrix that has an inverse. 4 -1 4 2 6. -4 2.
In Problem a system of linear equations and a reduced matrix for the system are given. (a) Use the reduced matrix to find the general solution of the system, if one exists. (b) If multiple
Problems 21 have nonunique solutions. If there is no solution, indicate this; if there are multiple solutions, find two different solutions. Use the simplex method, with x ≥ 0, y ≥ 0. 21.
In Problem perform the operations if possible.D – G
Suppose the technology matrix for a closed model of a simple economy is given by matrix A. Find the gross productions of the industries. NP H 0.4 0.3 0.4 Profit A = 0.2 0.4 0.2 Nonprofit 0.4 0.3 0.4
In Problem use matrices A through F. In Problem, perform the indicated operations when possible.Does (AAT)T = ATA? 1 2 1 1 A = 3 1 B = | 4 2 1 4 0 3 3 1 D=: 3 4 2 C = 1 5 1 E = 4 0. -1 3 F = 1 -1 -4
Find the inverse of 1 1 2 C = 1 1 0 -1 -1 -2 3.5 -2 -2.5 -0.5 2 2.5 -2 1.5 -1.5 1 -1 -3 3.
Use the matrices below as needed to complete Problems.Perform the indicated operations in ProblemsFI 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 | I =
In Problem perform the operations if possible.B + F
Use the following information in Problems. The national economy of Swiziland has four products: agricultural products, machinery, fuel, and steel. Producing 1 unit of agricultural products requires
In Problem use matrices A through F. In Problem, perform the indicated operations when possible.Are (CD)E and C(DE) equal? 1 2 1 1 A = 3 1 B = | 4 2 1 4 0 3 3 1 D=: 3 4 2 C = 1 5 1 E = 4 0. -1 3 F =
Use the matrices below as needed to complete Problems.DGT 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 | I = 3 F 4 11 -1 1 2. 2. 4. 6, ||
In Problem use the matrices below. Perform the indicated operations.ZCI 2 5 4 -1 1. A = 1 4 3 B = -5 8 -3 -2 -7 11 3 1. 3 4 1 C = C =1 7 -1 1 3 4 4 4 -8 1 D = -1 -1 2 F = -4 -3 -3 6. Z = 2. 1.
The systems of equations in Problem may have unique solutions, an infinite number of solutions, or no solution. Use matrices to find the general solution of each system, if a solution exists. x —
In Problems, solve each system using matrices. x - х — у =D3 x + y + 4z = 1 2х — Зу- 22 %3D 7
In Problem use the matrices below. Perform the indicated operations. IFZ 2 5 4 -1 1. A = 1 4 3 B = -5 8 -3 -2 -7 11 3 1. 3 4 1 C = C =1 7 -1 1 3 4 4 4 -8 1 D = -1 -1 2 F = -4 -3 -3 6. Z = 2. 1.
The systems of equations in Problem may have unique solutions, an infinite number of solutions, or no solution. Use matrices to find the general solution of each system, if a solution exists. -0.6x,
In Problems, solve each system using matrices. х — Зу + 2 %3D 4 2х — 5у - z 3 6
The tables below give the numbers of some species of threatened and endangered wildlife in the United States and in foreign countries in 2015.(a) Write a matrix A that contains the number of each of
Let matrix A represent the sales (in thousands of dollars) for the Walbash Company in 2018 in various cities, and let matrix B represent the sales (in thousands of dollars) for the same company in
Find the inverse of 1 4 4 B =|0 1 5 1 1 0.5 1 1.5 3. 3. 3. 2. 1, 3. 3. 2. 2. 3. 2.
Describe the procedure for finding the general solution of a system of linear equations if its reduced matrix indicates that it has an infinite number of solutions.
Use the matrices below as needed to complete Problems.Perform the indicated operations in ProblemsIF 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 | I =
In Problem perform the operations if possible.3B
Use the following information in Problems. The national economy of Swiziland has four products: agricultural products, machinery, fuel, and steel. Producing 1 unit of agricultural products requires
In Problem use matrices A through F. In Problem, perform the indicated operations when possible.Does CD = DC? 1 2 1 1 A = 3 1 B = | 4 2 1 4 0 3 3 1 D=: 3 4 2 C = 1 5 1 E = 4 0. -1 3 F = 1 -1 -4 3. 3.
In Problem perform the operations if possible.4D
A simple closed economy has the technology matrix A. Find the total outputs of the four sectors of the economy. Ag S F H 0.25 0.25 0.3 0.1 Agriculture 0.3 0.25 0.2 0.4 Steel A = 0.15 0.2 0.1 0.3 Fuel
In Problem use matrices A through F. In Problem, perform the indicated operations when possible.Are (1/4 A) B and ¼ (AB) equal? 1 2 1 1 A = 3 1 B = | 4 2 1 4 0 3 3 1 D=: 3 4 2 C = 1 5 1 E = 4 0. -1
Use the matrices below as needed to complete Problems.Perform the indicated operations in ProblemsDG(F) 4 2 -5 -5 -11 8 A = 3 -1 B 4 4 -3 -2 -2 1 4 -2 1 1 3 D = 1 1 E = 4 1 C = 2 1 3 6. G -1 -5 1 | I
In Problem perform the operations if possible.4C + 2D
In Problem perform the operations if possible.8C – 3D
In Problem perform the operations if possible.2A – 3B
Use the inverse found in Problem 13 to solve 1 1 1 0 1 1 1 y 2. 3. ||
The systems of equations in Problem may have unique solutions, an infinite number of solutions, or no solution. Use matrices to find the general solution of each system, if a solution exists. x - 3y
The systems of equations in Problem may have unique solutions, an infinite number of solutions, or no solution. Use matrices to find the general solution of each system, if a solution exists. 2x + y
In Problem perform the operations if possible.4F + 3G
The systems of equations in Problem may have unique solutions, an infinite number of solutions, or no solution. Use matrices to find the general solution of each system, if a solution exists. 5y + z
In Problem use the matrices below. Perform the indicated operations.F3 2 5 4 -1 1. A = 1 4 3 B = -5 8 -3 -2 -7 11 3 1. 3 4 1 C = C =1 7 -1 1 3 4 4 4 -8 1 D = -1 -1 2 F = -4 -3 -3 6. Z = 2. 1.
The systems of equations in Problem may have unique solutions, an infinite number of solutions, or no solution. Use matrices to find the general solution of each system, if a solution exists. 2x —
In Problem use the matrices below. Perform the indicated operations.AZ 2 5 4 -1 1. A = 1 4 3 B = -5 8 -3 -2 -7 11 3 1. 3 4 1 C = C =1 7 -1 1 3 4 4 4 -8 1 D = -1 -1 2 F = -4 -3 -3 6. Z = 2. 1.
The systems of equations in Problem may have unique solutions, an infinite number of solutions, or no solution. Use matrices to find the general solution of each system, if a solution exists. Sx + y
In Problem use the matrices below. Perform the indicated operations.AI 2 5 4 -1 1. A = 1 4 3 B = -5 8 -3 -2 -7 11 3 1. 3 4 1 C = C =1 7 -1 1 3 4 4 4 -8 1 D = -1 -1 2 F = -4 -3 -3 6. Z = 2. 1.
The systems of equations in Problem may have unique solutions, an infinite number of solutions, or no solution. Use matrices to find the general solution of each system, if a solution exists. 3x + 2y
In Problem use the matrices below. Perform the indicated operations.IA 2 5 4 -1 1. A = 1 4 3 B = -5 8 -3 -2 -7 11 3 1. 3 4 1 C = C =1 7 -1 1 3 4 4 4 -8 1 D = -1 -1 2 F = -4 -3 -3 6. Z = 2. 1.
The systems of equations in Problem may have unique solutions, an infinite number of solutions, or no solution. Use matrices to find the general solution of each system, if a solution exists. (3x
The systems of equations in Problem may have unique solutions, an infinite number of solutions, or no solution. Use matrices to find the general solution of each system, if a solution exists. 0.1x -
In Problems, solve each system using matrices. X1 + x2 + x3 + X4 = x1 - 2x2 + x3 - 4x4 = -5 - x3 + X4 X1 X2 + x3 + x4 = 2 3.

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