Explanation Given: The equations that describe the numbers of cars entering and leaving all intersections are, B: 3050 + x 1 = 2500 + x 2 C: 4100 + x 2 = x 3 + 2800 D: x 3 + 1800 = 3000 + x 4 A: x 4 + 2250 = x 1 + 2900 Where, the variables x 1 , x 2 , x 3 , and, x 4 have usual meaning as explained in question. 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: Combine the given four equation and form the system of four equations in four variables x 1 , x 2 , x 3 , and x 4 . { 3050 + x 1 = 2500 + x 2 4100 + x 2 = x 3 + 2800 x 3 + 1800 = 3000 + x 4 x 4 + 2250 = x 1 + 2900 The above system of equations is written as follows. { x 1 − x 2 = − 550 x 2 − x 3 = − 1300 x 3 − x 4 = 1200 − x 1 + x 4 = 650 The augmented matrix associated with the system of linear equations in x 1 , x 2 , x 3 , and x 4 is, [ 1 − 1 0 0 − 550 0 1 − 1 0 − 1300 0 0 1 − 1 1200 − 1 0 0 1 650 ] . Perform the row operation R 4 + R 1 → R 4 , and obtain the new row reduced matrix as, [ 1 − 1 0 0 − 550 0 1 − 1 0 − 1300 0 0 1 − 1 1200 0 − 1 0 1 100 ] Perform the row operation R 4 + R 2 → R 4 , and obtain the new row reduced matrix as, [ 1 − 1 0 0 − 550 0 1 − 1 0 − 1300 0 0 1 − 1 1200 0

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ISBN: 8220102019737

Author: YOCCO

Publisher: PEARSON

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Chapter 7.2, Problem 49E

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To solve: The system of the given four equations to find how traffic between the other intersections is related to the traffic from intersection D to intersection A.

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Chapter 7.2, Problem 48E

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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 system of the given four equations to find how traffic between the other intersections is related to the traffic from intersection D to intersection A.

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To solve: The system of the given four equations to find how traffic between the other intersections is related to the traffic from intersection D to intersection A.

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