Explanation Given: Clarrise has a total sum of $ 60 , 000 from which she invested twice as much in Bank B as in Bank A and Bank C. After one year, she earned a total interest of $ 1575 . Approach: The solution of the linear system will be obtained by putting the augmented matrix of the linear system into its reduced row-echelon form. Calculation: Let, Clarisse invest $ x , $ y , and $ z in bank A, B, and C, respectively. According to the given information, we get the following equations. x + y + z = 60 , 000 y = 2 ( x + z ) ⇒ 2 x − y + 2 z = 0 x ( 2 100 ) + y ( 2.5 100 ) + z ( 3 100 ) = 1575 ⇒ x 50 + y 40 + 3 z 100 = 1575 Considering this linear system, the augmented matrix is [ 1 1 1 60000 2 − 1 2 0 1 50 1 40 3 100 1575 ] . Transform the augmented matrix into row echelon form. Perform the transformation R 2 → R 2 − 2 R 1 . [ 1 1 1 60000 2 − 2 ( 1 ) − 1 − 2 ( 1 ) 2 − 2 ( 1 ) 0 − 2 ( 60000 ) 1 50 1 40 3 100 1575 ] → [ 1 1 1 60000 0 − 3 0 − 120000 1 50 1 40 3 100 1575 ] Perform the transformation R 3 → R 3 − R 1 50 . [ 1 1 1 60000 0 − 3 0 − 120000 1 50 − 1 50 1 40 − 1 50 3 100 − 1 50 1575 − 60000 50 ] → [ 1 1 1 60000 0 − 3 0 − 120000 0 1 200 1 100 375 ] Perform the transformation R 2 → − R 2 3 . [ 1 1 1 60000 0 ( − 1 3 ) − 3 ( − 1 3 ) 0 ( − 1 3 ) − 120000 ( − 1 3 ) 0 1 200 1 100 375 ] → [ 1 1 1 60000 0 1 0 40000 0 1 200 1 100 375 ] Perform the transformation R 3 → R 3 − 1 200 R 2

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ISBN: 8220100548512

Author: Watson

Publisher: CENGAGE L

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Chapter 11.CR, Problem 73E

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The amount of money Clarisse invested in bank A, B, and C.

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Chapter 11.CR, Problem 72E

Chapter 11.CR, Problem 74E

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Chapter 11 Solutions

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Ch. 11.1 - If a system of linear equations has infinitely...Ch. 11.1 - Write the augmented matrix of the following system...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - 5-10 Dimension of a Matrix State the dimension of...Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

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The amount of money Clarisse invested in bank A, B, and C.

Solution Summary: The author explains how Clarisse invested 2500 in Bank A, 40000 In Bank B, she earned a total interest of

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Chapter 11 Solutions

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The amount of money Clarisse invested in bank A, B, and C.