Each of the following 3 topics must be addressed: 1. Demonstrate how to use Excel to...
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Each of the following 3 topics must be addressed: 1. Demonstrate how to use Excel to solve a system of linear equations using matrices. Example: The average annual return (over 5-year period prior to May 1, 2013) of three mutual funds offered by AXA Equitable is shown in the table: Mutual Fund Moderate Allocations Average Annual Return 8.85% Equity 500 Index 16.00% Barclays U.S. Aggregate Bond Index 4.21% Source: https://www.sec.gov/Archives/edgar/data/1160168/000119312513192136/d523412d497.htm Suppose you have $10,000 to invest in these three funds. You want to invest $200 more in the Moderate Allocations fund that you will in the Equity 500 Index fund. a. Assuming the accounts will earn the annual rates shown, how much should you invest for a year in each fund if you want average return to be 9%? b. How much should you invest in each fund if you want your average return to be 10%? c. How much if you want 12%? 2. Demonstrate how to use Excel to encrypt or code a message using matrices and their inverse. Example: The message to be encoded is SEPTEBMER IS HERE The encoded message to be formed using triplets of numbers and the 3x3 matrix 1 0 01 1 A = 3 1 5 whose inverse is A- -201 -1 = 0 0 -13 1 -5 2 0 1 Use the following association of letters and divide the message into triplets of letters: SEP TEM BER ISH ERE A B U C D E 0 1 2 D3 FGH I J K 4 5 6 7 8 9 10 L M N 11 12 13 O P Q R S T U 14 15 16 17 18 19 20 21 22 23 24 25 12 > W W X Y N Now multiply the matrix A times each column vector of the message. You will receive the coded message. To decode the message, form 3x1 column vectors of the numbers in the coded message and multiply on the left by A-. 3. Demonstrate how to use Excel to add and multiply matrices to prove the following properties of matrices a. Cumulative property for addition: A + B = B + A b. Associative property for addition: A + (B + C) = (A + B) + C c. Associative property of matrix multiplication A(BC) = (AB)C d. Distributive property of matrix multiplication A(B + C) = AB + AC e. Identity property IA = A and AI = A Each of the following 3 topics must be addressed: 1. Demonstrate how to use Excel to solve a system of linear equations using matrices. Example: The average annual return (over 5-year period prior to May 1, 2013) of three mutual funds offered by AXA Equitable is shown in the table: Mutual Fund Moderate Allocations Average Annual Return 8.85% Equity 500 Index 16.00% Barclays U.S. Aggregate Bond Index 4.21% Source: https://www.sec.gov/Archives/edgar/data/1160168/000119312513192136/d523412d497.htm Suppose you have $10,000 to invest in these three funds. You want to invest $200 more in the Moderate Allocations fund that you will in the Equity 500 Index fund. a. Assuming the accounts will earn the annual rates shown, how much should you invest for a year in each fund if you want average return to be 9%? b. How much should you invest in each fund if you want your average return to be 10%? c. How much if you want 12%? 2. Demonstrate how to use Excel to encrypt or code a message using matrices and their inverse. Example: The message to be encoded is SEPTEBMER IS HERE The encoded message to be formed using triplets of numbers and the 3x3 matrix 1 0 01 1 A = 3 1 5 whose inverse is A- -201 -1 = 0 0 -13 1 -5 2 0 1 Use the following association of letters and divide the message into triplets of letters: SEP TEM BER ISH ERE A B U C D E 0 1 2 D3 FGH I J K 4 5 6 7 8 9 10 L M N 11 12 13 O P Q R S T U 14 15 16 17 18 19 20 21 22 23 24 25 12 > W W X Y N Now multiply the matrix A times each column vector of the message. You will receive the coded message. To decode the message, form 3x1 column vectors of the numbers in the coded message and multiply on the left by A-. 3. Demonstrate how to use Excel to add and multiply matrices to prove the following properties of matrices a. Cumulative property for addition: A + B = B + A b. Associative property for addition: A + (B + C) = (A + B) + C c. Associative property of matrix multiplication A(BC) = (AB)C d. Distributive property of matrix multiplication A(B + C) = AB + AC e. Identity property IA = A and AI = A
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Related Book For
Discovering Advanced Algebra An Investigative Approach
ISBN: 978-1559539845
1st edition
Authors: Jerald Murdock, Ellen Kamischke, Eric Kamischke
Posted Date:
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