Explanation Definition used: 1. Any augmented matrix that has 1`s or 0`s on the diagonal of its coefficient part and 0`s below the diagonal is said to be in row-echelon form. 2. The augmented matrix representing n equations in n variables is said to be in reduced row-echelon form if it has 1`s or 0`s on the diagonal of its coefficient part and 0`s everywhere else. Calculation: Let x represent the cost of property I, y represent the cost of property II and z represent the cost of property III. The total amount of money a bank lends us given by, $1,180,000. Thus, x + y + z = 1 , 180 , 000 . Let us assume that the cost of property I is more than of the property II by $75,000. That is, x = y + 75 , 000 . Given that, the third property costs three times the sum of other two properties. That is, z = 3 ( x + y ) . Combine the above three equations and form the system of three equations in three variables x , y and z as follows. { x + y + z = 1 , 180 , 000 x = y + 75 , 000 z = 3 ( x + y ) Simplify the above system and rewrite as follows. { x + y + z = 1 , 180 , 000 x − y = 75 , 000 3 x + 3 y − z = 0 The augmented matrix associated with the system of linear equations in x , y and z is, [ 1 1 1 1 , 180 , 000 1 − 1 0 75 , 000 3 3 − 1 0 ] Observe that the augmented matrix is not in row-echelon form. Hence apply certain row operations and reduce into row-echelon form as follows

5th Edition

ISBN: 9780134179926

Author: HARSHBARGER

Publisher: PEARSON CO

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Chapter 7, Problem 39RE

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To find: The cost of each property.

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Chapter 7, Problem 38RE

Chapter 7, Problem 40RE

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Ch. 7.1 - In Exercises 14, solve the systems of equations....Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

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The cost of each property.

Solution Summary: The author explains that the cost of property I, II, and III is 185,000.

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To find: The cost of each property.

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