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CalculusFinite Mathematics and Applied Calculus (MindTap Course List)In Exercises 5–12, you are given a technology matrix A and an external demand vector D. Find the corresponding production vector X. [ HinT: See Quick Example 1.] A = [ 0.5 0.1 0 0 0.5 0.1 0 0 0.5 ] , D = [ 3 , 000 3 , 800 2 , 000 ]BuyFind*arrow_forward*

7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337274203

Chapter 5.5, Problem 10E

Textbook Problem

In Exercises 5–12, you are given a technology matrix A and an external demand vector D. Find the corresponding production vector X. [**HinT:** See Quick Example 1.]

Expert Solution

To determine

**To calculate:** The production vector where the technology matrix is

**Given Information:**

The technology matrix is

**Formula used:**

According to the product rule of matrices, the matrix *X* with dimension *Y* with dimension *XY* is the matrix of dimension *AB* is the sum of product of corresponding entries of row *X* and column *j* of *Y*.

When a matrix has *m* rows and *n* columns, then the matrix is said to have dimension of

For two matrices *A* and *B* with equal dimension, the sum of difference is simplified as,

If the matrix obtained after row reduction has identity matrix on the left side then the matrix obtained on the right is the required inverse of *A* otherwise *A* is singular.

**Calculation:**

Consider technology matrix is

As, the production vector *X* satisfies *A* is the technology matrix, *D* is the demand vector and *I* is the identity matrix.

Substitute *A*, *I*, and *D* in

It is known that a matrix with *m* rows and *n* columns is of dimension *m* and *n* are positive integers.

Since, number of rows in the matrix

Substitute *m* and *n* in

Thus, dimension of the matrix

Since, number of rows in the matrix

Substitute *m* and *n* in

Thus, dimension of the matrix

Thus, both the matrices have same dimensions.

Since, number of rows in the matrix

Substitute *m* and *n* in

Thus, dimension of

It is known that for two matrices *A* and *B* with equal dimension,

Simplify

Consider,

Finite Mathematics and Applied Calculus (MindTap Course List)

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Probability and Statistics for Engineering and the Sciences

Simplify the expressions in Exercises 97106. y5/4y3/4

Finite Mathematics

State the four steps of Polyas four-step problem-solving strategy.

Mathematical Excursions (MindTap Course List)

Find each product: (23x2y2)(916xy2)

Elementary Technical Mathematics

In Exercises 9 and 10, classify the triangle not shown by considering the measures of its angles. a All angles ...

Elementary Geometry For College Students, 7e

Divide the following fractions and mixed numbers.
a. b. c.

Contemporary Mathematics for Business & Consumers

In Problems 19-44, factor completely.
43.

Mathematical Applications for the Management, Life, and Social Sciences

If a, b, c, and d are constants such that limxax2+sinbx+sincx+sindx3x2+5x4+7x6=8 find the value of the sum a + ...

Single Variable Calculus: Early Transcendentals

Finding the Angle of Inclination of a Tangent Plane In Exercises 33-36, find the angle of inclination of the ta...

Calculus: Early Transcendental Functions (MindTap Course List)

Finding the Volume of a Solid In Exercises 25-32, find the volume of the solid generated by revolving the regio...

Calculus of a Single Variable

Graph one complete cycle of each of the following. In each case, label the axes accurately and identify the ver...

Trigonometry (MindTap Course List)

Prove that if , , and , then .

Elements Of Modern Algebra

For what value of n is the nth partial sum within 0.01 of the value of ? (Choose the smallest such n.)
n = 4
n ...

Study Guide for Stewart's Multivariable Calculus, 8th

True or False:
If Tn(x) is the nth Taylor polynomial for f(x) centered at c, then Tn(k)(c) = f(k)(c) for k = 0,...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

In Exercise 9-14, state whether the statements are true or false. {Chevrolet,Cadillac,Buick}{xxisadivisionofGen...

Finite Mathematics for the Managerial, Life, and Social Sciences

Gallup surveyed adult Americans about their consumer debt (Americans Big Debt Burden Growing, Not Evenly Distri...

Introduction To Statistics And Data Analysis

In Exercises 25 to 32, name the type of reasoning if any used. You believe that Anyone who plays major league b...

Elementary Geometry for College Students

Maximum ProfitA corporation manufactures digital camera at two locations. The cost of producing x1 units at loc...

Multivariable Calculus

Volume In Exercises 75 and 76, find the volume of the solid generated by revolving the region bounded by the gr...

Calculus (MindTap Course List)

Solve the following exercises using the Law of Cosines. Find side x. All dimensions are in inches.

Mathematics For Machine Technology

Self check Graph: fx=log6x

College Algebra (MindTap Course List)

In addition to the key words, you should also be able to define each of the following terms: Ethics Nuremberg C...

Research Methods for the Behavioral Sciences (MindTap Course List)

Although researchers typically begin a single-case reversal study with the intention of using an ABAB design, w...

Research Methods for the Behavioral Sciences (MindTap Course List)

Major League Baseball franchises rely on attendance for a large share of their total revenue, and weekend games...

Statistics for Business & Economics, Revised (MindTap Course List)

In exercise 4, the following estimated regression equation relating sales to inventory investment and advertisi...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Design your own fractal. Discuss its self-similarity and its recursive nature. Find its perimeter and area or i...

Mathematics: A Practical Odyssey

(a) Verify that the one-parameter family y2 2y = x2 x + c is an implicit solution of the differential equatio...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

Reminder Round all answers to two decimal places unless otherwise indicated. Data That Are Not Exponential Show...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Make a trace table to trace the action of Algorithm 4.10.2 for the input variables given in 17-19. 19. 1,570 an...

Discrete Mathematics With Applications

Case Problem Lawsuit Defense Strategy
John Campbell, an employee of Manhattan Construction Company, claims to h...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Returns on Mutual Finds. The Wall Street Journal provides the net asset value, the year-to-date percent return,...

Essentials Of Statistics For Business & Economics

In the following exercises, evaluate the limit algebraically or explain why the limit does not exist. 215. limx...

Calculus Volume 1

In the following exercises, evaluate each integral in terms of an inverse trigonometric function. 392. 1/21/2dx...

Calculus Volume 2