Explanation Given Information: The total amount invested is $ 6 , 000 at beginning of 2011 where the amount is equal in SH and MMY and the total year-to-date loss is $ 360 . The performance of the 3 funds are given as, Year-to-Date Loss (%) MYY (ProShares Short Midcap 400) 6 SH (ProShares Short S&P 500) 5 REW (ProShares UltraShort Technology) 7 Formula used: The matrix equation is, A X = B Where, A is the matrix that has entries equal to the coefficients of the left hand side of the system of equations and X is the column matrix of the unknowns in the system and B is the column matrix and has entries equal to the coefficients of the right hand side of the system of equations. The matrix property, 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. For matrices A with dimension m × n and B with dimension n × k , the product AB is the matrix of dimension m × k and ij th entry of AB is the sum of product of corresponding entries of row i of A and column j of B . Calculation: Consider the performance of the 3 funds, Year-to-Date Loss (%) MYY (ProShares Short Midcap 400) 6 SH (ProShares Short S&P 500) 5 REW (ProShares UltraShort Technology) 7 Let x be the amount invested in MYY, y be the amount in SH and z be the amount in REW. Since, the total investment is $ 6 , 000 . Thus, x + y + z = 6 , 000 . Since, the amount invested in MYY and SH are equal. Thus, x − y = 0 . Since, the total year-to-date loss is $ 360 and the year-to-date loss from the table is 0.06 in MYY, 0.05 in SH and 0.07 in REW. Thus, 0.06 x + 0.05 y + 0.07 = 360 . Therefore, the system of linear equations is, x + y + z = 6 , 000 x − y = 0 0.06 x + 0.05 y + 0.07 z = 360 Thus, A = [ 1 1 1 1 − 1 0 0.06 0.05 0.07 ] , X = [ x y z ] and B = [ 6 , 000 0 360 ] . Hence, the matrix equation is [ 1 1 1 1 − 1 0 0.06 0.05 0.07 ] [ x y z ] = [ 6 , 000 0 360 ] . Solve the equation for X . 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 A − 1 = I and A − 1 A = I , where I is the n × n identity matrix. Substitute I for A − 1 A in A − 1 A X = A − 1 B and simplify. 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 1 − 1 0 0.06 0.05 0.07 ] − 1 [ 6 , 000 0 360 ] . Consider the matrix [ 1 1 1 1 − 1 0 0.06 0.05 0.07 ] . Since, number of rows in [ 1 1 1 1 − 1 0 0.06 0.05 0.07 ] is 3 and number of columns is 3 . Thus, dimension of [ 1 1 1 1 − 1 0 0.06 0.05 0.07 ] is 3 × 3 . Thus, the augmented matrix is, [ 1 1 1 1 0 0 1 − 1 0 0 1 0 0.06 0.05 0.07 0 0 1 ] . Row reduce the matrix [ 1 1 1 1 0 0 1 − 1 0 0 1 0 0.06 0.05 0.07 0 0 1 ] . Perform the row operation R 3 → R 3 − 0.06 R 1 and R 2 → R 2 − R 1 , [ 1 1 1 1 0 0 1 − 1 0 0 1 0 0.06 0.05 0.07 0 0 1 ] → [ 1 1 1 1 0 0 0 − 2 − 1 − 1 1 0 0 − 0.01 0.01 − 0.06 0 1 ] Perform the row operations R 1 → 2 R 1 + R 2 and R 3 → 2 R 3 − 0.01 R 2 , [ 1 1 1 1 0 0 0 − 2 − 1 − 1 1 0 0 − 0.01 0.01 − 0.06 0 1 ] → [ 2 0 1 1 1 0 0 − 2 − 1 − 1 1 0 0 0 0.03 − 0.11 − 0.01 2 ] Perform the row operations R 1 → R 1 − ( 100 3 ) R 3 , R 2 → R 2 + ( 100 3 ) R 3 and R 3 → ( 100 3 ) R 3 [ 2 0 1 1 1 0 0 − 2 − 1 − 1 1 0 0 0 0.03 − 0.11 − 0.01 2 ] → [ 2 0 0 14 3 4 3 − 200 3 0 − 2 0 − 14 3 2 3 200 3 0 0 1 − 11 3 − 1 3 200 3 ] Perform the row operations R 1 → ( 1 2 ) R 1 and R 1 → − ( 1 2 ) R 1 , [ 2 0 0 14 3 4 3 − 200 3 0 − 2 0 − 14 3 2 3 200 3 0 0 1 − 11 3 − 1 3 200 3 ] → [ 1 0 0 7 3 2 3 − 100 3 0 1 0 7 3 − 1 3 − 100 3 0 0 1 − 11 3 − 1 3 200 3 ] Therefore, [ 1 1 1 1 − 1 0 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 5.3, Problem 56E

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To calculate: The amount investment in each of the 3 funds if the total amount invested is $6,000 at beginning of 2011 where the amount is equal in SH and MMY and the total year-to-date loss is $360.

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Chapter 5.3, Problem 55E

Chapter 5.3, Problem 57E

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Chapter 5 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

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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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The amount investment in each of the 3 funds if the total amount invested is $ 6 , 000 at beginning of 2011 where the amount is equal in SH and MMY and the total year-to-date loss is $ 360 .

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To calculate: The amount investment in each of the 3 funds if the total amount invested is $6,000 at beginning of 2011 where the amount is equal in SH and MMY and the total year-to-date loss is $360.

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Chapter 5 Solutions