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 And the amount invested by the company in DSV stock is $150,000 and for the amount of $600, dividends of 20 c per share was paid on July 15. 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: First find the number of shares purchased on July 1, August 1 and September 1. 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 0.1 0 1 0 0 0 0 5 ] → [ 1 1 1 1 0 0 0 − 2 0 − 4 0.1 15 1 0 0 0 0 5 ] Perform the row operations R 2 → − 1 2 R 2 and R 3 → R 3 + R 1 , [ 1 1 1 1 0 0 0 − 2 0 − 4 0.1 15 1 0 0 0 0 5 ] → [ 1 1 1 1 0 0 0 1 0 2 − 0

7th Edition

ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 4, Problem 38RE

To determine

To calculate: The total loss from the Duffin stock debacle when per share selling price of DSV is $20 on October 15 and OHaganBooks.com sold 3,000 shares. Also, DSV has announced a two for one split which means each share was converted into two shares and additional dividend paid by the company on October 1 is 10c. The provided table is 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

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Chapter 4, Problem 37RE

Chapter 4, Problem 39RE

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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 total loss from the Duffin stock debacle when per share selling price of DSV is 20 on October 15 and OHaganBooks.com sold 3,000 shares.

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