Explanation Given Information: The total money invested is $ 5 , 000 and money invested in a traditional account paying 1 % , a certificate of deposits paying 3.6 % ; and a prepaid college plan paying 5.5 % and wanted to collect $ 195 from investment and money invested in prepaid college plan is same as that invested in other two plans together. Formula Used: The following elementary row operations may be performed on an augmented matrix to get reduced row echelon form: Step1: Swap any two rows if required. Step2: Multiply the row by the desired non-zero number. Step3: Now, add multiples of another row beneath or above it to change the row being operated. Gauss-Jorden elimination method is used to convert the system of linear equations into diagonal form by using the above three row operations repeatedly. Calculation: Let x represents the money invested in traditional account, y represents the money invested in certificate of deposits and z represents the money invested in prepaid college plan. Consider that the provided total money invested is $ 5 , 000 . Thus, the equation will be, x + y + z = 5 , 000 . Also, consider that the provided money invested in a traditional account paying 1 % , a certificate of deposits paying 3.6 % ; and a prepaid college plan paying 5.5 % and wanted to collect $ 195 from investment. Thus, the equation will be, 0.01 x + 0.036 y + 0.055 z = 195 . A provided condition is, if they want to invest the same amount in the prepaid college fund as in the other two plans together, Thus, the equation will be, z = x + y or − x − y + z = 0 , So, the system of linear equations formed is { x + y + z = 5 , 000 0.01 x + 0.036 y + 0.055 z = 8 , 000 − x − y + z = 0 The equivalent augmented matrix is [ 1 1 1 5 , 000 0.01 0.036 0.055 195 − 1 − 1 1 0 ] . Compute the augmented matrix as follows: Multiply row 1 by − 0.01 and add the result to row 2 and add row 1 to row 3 . [ 1 1 1 5 , 000 0.01 0.036 0.055 195 − 1 − 1 1 0 ] → R 3 + R 1 R 2 + ( − 0.01 ) R 1 [ 1 1 1 5 , 000 0 0.026 0.045 145 0 0 2 5 , 000 ] Multiply row 2 by 1 0.026 to get a leading 1 . [ 1 1 1 5 , 000 0 0.026 0.045 145 0 0 2 5 , 000 ] → 1 0.026 R 2 [ 1 1 1 5 , 000 0 1 45 26 72500 13 0 0 2 5 , 000 ] Multiply row 2 by − 1 and add the result to row 1

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

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Chapter 2.1, Problem 76E

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To calculate: The investment made by Jim and Lucy in three different plans if the total money invested is $5,000 and different types of plans are: a traditional account paying 1%, a certificate of deposits paying 3.6%; and a prepaid college plan paying 5.5% and wanted to collect $195 from investment and money invested in prepaid college plan is same as that invested in other two plans together.

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Chapter 2.1, Problem 75E

Chapter 2.1, Problem 77E

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Chapter 2 Solutions

Finite Mathematics & Its Applications (12th Edition)

Ch. 2.1 - 1. Determine whether the following systems of...Ch. 2.1 - Give the meaning of each of the following...Ch. 2.1 - 3. Perform the indicated elementary row...Ch. 2.1 - State the next elementary row operation that...Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - Prob. 2E Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - In Exercises 18, perform the indicated elementary...Ch. 2.1 - In Exercises 18, perform the indicated elementary...

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Solution Summary: The author explains the Gauss-Jorden elimination method used to convert the system of linear equations into diagonal form by using the above three row operations repeatedly.

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