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

7th Edition

ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Question

Chapter 4, 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 4, Problem 35RE

Chapter 4, Problem 37RE

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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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