Explanation Given Information: The table is provided below, Date Number of Shares: DHP Price per Share: DHP Number of Shares: DSV Price per Share: DSV July 1 ? $20 ? $10 August 1 ? $10 ? $20 September 1 ? $5 ? $40 Total 5,000 7,000 Formula used: The matrix equation is, A X = B Where, the matrix A has entries equal to the coefficients of the left hand side of the system of equations and the matrix X is the column matrix of the unknowns in the system and the matrix B is the column matrix and has entries equal to the coefficients of the right hand side of the system of equations. The inverse property of matrices, A A − 1 = I and A − 1 A = I Where, I is the n × n identity matrix. Two matrices A and B are equal if they have same dimensions and their corresponding entries are equal. Calculation: Consider the provided table, Now let x be the number of shares purchased on July 1, y be the number of shares purchased on August 1, z be the number of shares purchased on September 1. Now consider total number of purchased shares, $7,000 and write the equation using x, y and z as, x + y + z = 7 , 000 And consider total investment, $150,000 and write the equation using x, y and z as, 10 x + 20 y + 40 z = 150 , 000 Now consider total amount of dividends, $600 and per share dividend, 20 c paid on July 15, and write the equation using x, y and z as, 0.20 x = 600 Now the three equations are, x + y + z = 7 , 000 10 x + 20 y + 40 z = 150 , 000 0.20 x = 600 For the matrix equation, A = [ 1 1 1 10 20 40 0.2 0 0 ] , X = [ x y z ] and B = [ 7 , 000 150 , 000 600 ] . Thus, the matrix equation is [ 1 1 1 10 20 40 0.2 0 0 ] [ x y z ] = [ 7 , 000 150 , 000 600 ] . Consider the equation A X = B . Multiply both sides on the left of the equation by A − 1 , A − 1 A X = A − 1 B As A − 1 A = I , so substitute I for A − 1 A in A − 1 A X = A − 1 B and simplify as below, A − 1 A X = A − 1 B I X = A − 1 B X = A − 1 B Thus, the equation is [ x y z ] = [ 1 1 1 10 20 40 0.2 0 0 ] − 1 [ 7 , 000 150 , 000 600 ] . Consider the matrix [ 1 1 1 10 20 40 0.2 0 0 ] . Since, number of rows in [ 1 1 1 10 20 40 0.2 0 0 ] is 3 and number of columns is 3 , dimension of [ 1 1 1 10 20 40 0.2 0 0 ] is 3 × 3 Augmented matrix with the 3 × 3 identity matrix [ 1 0 0 0 1 0 0 0 1 ] is [ 1 1 1 1 0 0 10 20 40 0 1 0 0.2 0 0 0 0 1 ] . Now reduce the matrix [ 1 1 1 1 0 0 10 20 40 0 1 0 0.2 0 0 0 0 1 ] as below, Perform the row operation R 3 → 5 R 3 and R 2 → 1 10 R 2 , [ 1 1 1 1 0 0 10 20 40 0 1 0 0.2 0 0 0 0 1 ] → [ 1 1 1 1 0 0 1 2 4 0 0.1 0 1 0 0 0 0 5 ] Perform the row operations R 2 → R 2 − 4 R 1 , [ 1 1 1 1 0 0 1 2 4 0 0.1 0 1 0 0 0 0 5 ] → [ 1 1 1 1 0 0 − 3 − 2 0 − 4 0.1 0 1 0 0 0 0 5 ] Perform the row operations R 2 → R 2 + 3 R 3 , [ 1 1 1 1 0 0 − 3 − 2 0 − 4 0

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 5, Problem 36RE

To determine

To calculate: The number of shares purchased by DSV OHaganBooks.com on the dates provided in the table by the use of matrix inversion. The amount invested by the company in DSV stock is $150,000 and for the amount of $600, dividends of 20c per share was paid on July 15.

Date Number of Shares: DHP Price per Share: DHP Number of Shares: DSV Price per Share: DSV

July 1 ? $20 ? $10

August 1 ? $10 ? $20

September 1 ? $5 ? $40

Total 5,000 7,000

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Chapter 5, Problem 35RE

Chapter 5, Problem 37RE

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Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 5.1 - In Exercises 110, find the dimensions of the given...Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - In Exercises 110, find the dimensions of the given...Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

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(You...Ch. 5.3 - Prob. 77E Ch. 5.3 - Prob. 78E Ch. 5.4 - Prob. 1E Ch. 5.4 - Prob. 2E Ch. 5.4 - Prob. 3E Ch. 5.4 - Prob. 4E Ch. 5.4 - Prob. 5E Ch. 5.4 - Prob. 6E Ch. 5.4 - Prob. 7E Ch. 5.4 - Prob. 8E Ch. 5.4 - Prob. 9E Ch. 5.4 - In Exercises 914, reduce the given payoff matrix...Ch. 5.4 - In Exercises 914, reduce the given payoff matrix...Ch. 5.4 - In Exercises 914, reduce the given payoff matrix...Ch. 5.4 - Prob. 13E Ch. 5.4 - Prob. 14E Ch. 5.4 - Prob. 15E Ch. 5.4 - Prob. 16E Ch. 5.4 - Prob. 17E Ch. 5.4 - Prob. 18E Ch. 5.4 - Prob. 19E Ch. 5.4 - Prob. 20E Ch. 5.4 - Prob. 21E Ch. 5.4 - Prob. 22E Ch. 5.4 - Prob. 23E Ch. 5.4 - Prob. 24E Ch. 5.4 - Prob. 25E Ch. 5.4 - Prob. 26E Ch. 5.4 - Prob. 27E Ch. 5.4 - Prob. 28E Ch. 5.4 - In Exercises 2532, set up the payoff matrix....Ch. 5.4 - In Exercises 2532, set up the payoff matrix....Ch. 5.4 - In Exercises 2532, set up the payoff matrix....Ch. 5.4 - Prob. 32E Ch. 5.4 - Prob. 33E Ch. 5.4 - More Retail Discount Wars Your Abercrom B mens...Ch. 5.4 - Factory Location22 A manufacturer of electrical...Ch. 5.4 - Crop Choice23 A farmer has a choice of growing...Ch. 5.4 - Study Techniques Your mathematics test is tomorrow...Ch. 5.4 - Prob. 38E Ch. 5.4 - Prob. 39E Ch. 5.4 - Prob. 40E Ch. 5.4 - Prob. 41E Ch. 5.4 - Prob. 42E Ch. 5.4 - Prob. 43E Ch. 5.4 - Prob. 44E Ch. 5.4 - Prob. 45E Ch. 5.4 - Prob. 46E Ch. 5.4 - Prob. 47E Ch. 5.4 - Prob. 48E Ch. 5.4 - Campaign Strategies27 Florida and Ohio are swing...Ch. 5.4 - Prob. 50E Ch. 5.4 - Prob. 51E Ch. 5.4 - Prob. 52E Ch. 5.4 - Prob. 53E Ch. 5.4 - Prob. 54E Ch. 5.4 - Prob. 55E Ch. 5.4 - Exercises 37 and 38 seem to suggest that studying...Ch. 5.4 - Prob. 57E Ch. 5.4 - Prob. 58E Ch. 5.5 - Let A be the technology matrix A=[0.20.050.80.01],...Ch. 5.5 - Let A be the technology matrix...Ch. 5.5 - Prob. 3E Ch. 5.5 - Prob. 4E Ch. 5.5 - Prob. 5E Ch. 5.5 - In Exercises 512, you are given a technology...Ch. 5.5 - In Exercises 512, you are given a technology...Ch. 5.5 - In Exercises 512, you are given a technology...Ch. 5.5 - In Exercises 512, you are given a technology...Ch. 5.5 - In Exercises 512, you are given a technology...Ch. 5.5 - In Exercises 512, you are given a technology...Ch. 5.5 - In Exercises 512, you are given a technology...Ch. 5.5 - Given A=[0.10.40.20.5], find the changes in...Ch. 5.5 - Prob. 14E Ch. 5.5 - Prob. 15E Ch. 5.5 - Prob. 16E Ch. 5.5 - Prob. 17E Ch. 5.5 - Prob. 18E Ch. 5.5 - Campus Food The two campus cafeterias, the Main...Ch. 5.5 - Plagiarism Two student groups at Enormous State...Ch. 5.5 - Prob. 21E Ch. 5.5 - Wood and Paper Two sectors of the U.S. economy are...Ch. 5.5 - Prob. 23E Ch. 5.5 - Prob. 24E Ch. 5.5 - Prob. 25E Ch. 5.5 - Prob. 26E Ch. 5.5 - Prob. 27E Ch. 5.5 - Prob. 28E Ch. 5.5 - Prob. 29E Ch. 5.5 - Prob. 30E Ch. 5.5 - Exercises 3134 require the use of technology....Ch. 5.5 - Exercises 3134 require the use of technology....Ch. 5.5 - Prob. 33E Ch. 5.5 - Prob. 34E Ch. 5.5 - Prob. 35E Ch. 5.5 - Prob. 36E Ch. 5.5 - What would it mean if the total output figure for...Ch. 5.5 - Prob. 38E Ch. 5.5 - Prob. 39E Ch. 5.5 - Prob. 40E Ch. 5.5 - Prob. 41E Ch. 5.5 - Prob. 42E Ch. 5 - For Exercises 110, let...Ch. 5 - Prob. 2RE Ch. 5 - Prob. 3RE Ch. 5 - Prob. 4RE Ch. 5 - For Exercises 110, let...Ch. 5 - Prob. 6RE Ch. 5 - Prob. 7RE Ch. 5 - Prob. 8RE Ch. 5 - Prob. 9RE Ch. 5 - Prob. 10RE Ch. 5 - Prob. 11RE Ch. 5 - Prob. 12RE Ch. 5 - Prob. 13RE Ch. 5 - Prob. 14RE Ch. 5 - Prob. 15RE Ch. 5 - Prob. 16RE Ch. 5 - Prob. 17RE Ch. 5 - Prob. 18RE Ch. 5 - In Exercises 1720, write the given system of...Ch. 5 - Prob. 20RE Ch. 5 - Prob. 21RE Ch. 5 - Prob. 22RE Ch. 5 - Prob. 23RE Ch. 5 - Prob. 24RE Ch. 5 - In Exercises 2528, find the production vector X...Ch. 5 - Prob. 26RE Ch. 5 - Prob. 27RE Ch. 5 - Prob. 28RE Ch. 5 - Prob. 29RE Ch. 5 - Prob. 30RE Ch. 5 - Prob. 31RE Ch. 5 - Prob. 32RE Ch. 5 - It is now July 1, and online sales of romance,...Ch. 5 - Prob. 34RE Ch. 5 - Prob. 35RE Ch. 5 - Prob. 36RE Ch. 5 - Prob. 37RE Ch. 5 - Prob. 38RE Ch. 5 - OHaganBooks.com has two main...Ch. 5 - Prob. 40RE Ch. 5 - OHaganBooks.com has two main...Ch. 5 - Prob. 42RE Ch. 5 - Prob. 43RE Ch. 5 - Prob. 44RE Ch. 5 - Prob. 45RE Ch. 5 - Prob. 46RE Ch. 5 - Prob. 47RE Ch. 5 - Prob. 48RE Ch. 5 - Prob. 49RE Ch. 5 - Some of the books sold by OHaganBooks.com are...Ch. 5 - Some of the books sold by OHaganBooks.com are...Ch. 5 - Some of the books sold by OHaganBooks.com are...

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Date	Number of Shares: DHP	Price per Share: DHP	Number of Shares: DSV	Price per Share: DSV
July 1	?	$20	?	$10
August 1	?	$10	?	$20
September 1	?	$5	?	$40
Total	5,000		7,000

Solution Summary: The author calculates the number of shares purchased by DSV OHaganBooks.com on the dates provided in the table using matrix inversion.

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