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. Given that, the total cost is $375,000. Thus, x + y + z = 375 , 000 . Let us assume that the cost of property I is more than of the property II by $50,000. That is, x = y + 50 , 000 . Given that, the third cost is half the sum of other two properties. That is, z = 1 2 ( 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 = 375 , 000 x = y + 50 , 000 z = 1 2 ( x + y ) Simplify the above system and rewrite as follows. { x + y + z = 375 , 000 x − y = 50 , 000 x + y − 2 z = 0 The augmented matrix associated with the system of linear equations in x , y and z is, [ 1 1 1 375 , 000 1 − 1 0 50 , 000 1 1 − 2 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

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ISBN: 8220103453592

Author: YOCCO

Publisher: Pearson Education (US)

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Chapter 7, Problem 41RE

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Chapter 7 Solutions

EBK COLLEGE ALGEBRA IN CONTEXT

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 business property.

Solution Summary: The author explains that the cost of each business property is x, y, and z.

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