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Problem 1.2. In each of the following traffic networks consisting of one- way streets, a number along an edge refers to the number of cars per hour passing through the street in the indicated direction. For each network, write down a linear system whose solutions give the possible tuples of values for the traffic flow (cars per hour) passing through the unlabelled edges in the indicated direction in the network. (You don't need to solve the systems.) (a) (b) 200 300 50 200 150 200 150 100 300 50 200

Problem 1.2. In each of the following traffic networks consisting of one- way streets, a number along an edge refers to the number of cars per hour passing through the street in the indicated direction. For each network, write down a linear system whose solutions give the possible tuples of values for the traffic flow (cars per hour) passing through the unlabelled edges in the indicated direction in the network. (You don't need to solve the systems.) (a) (b) 200 300 50 200 150 200 150 100 300 50 200

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 1.2. In each of the following traffic networks consisting of one- way streets, a number along an edge refers to the number of cars per hour passing through the street in the indicated direction. For each network, write down a linear system whose solutions give the possible tuples of values for the traffic flow (cars per hour) passing through the unlabelled edges in the indicated direction in the network. (You don't need to solve the systems.) (a) (b) 200 300 50 200 150 200 150 100 300 50 Problem 1.3. For invertible square matrices A,B,C of the same size, (a) prove that C-¹B-¹A-¹ is the inverse of ABC and (b) assuming AB = BA, prove that (A + B)³ = A³ +3A²B+3AB² + B³. 200
Transcribed Image Text:Problem 1.2. In each of the following traffic networks consisting of one- way streets, a number along an edge refers to the number of cars per hour passing through the street in the indicated direction. For each network, write down a linear system whose solutions give the possible tuples of values for the traffic flow (cars per hour) passing through the unlabelled edges in the indicated direction in the network. (You don't need to solve the systems.) (a) (b) 200 300 50 200 150 200 150 100 300 50 Problem 1.3. For invertible square matrices A,B,C of the same size, (a) prove that C-¹B-¹A-¹ is the inverse of ABC and (b) assuming AB = BA, prove that (A + B)³ = A³ +3A²B+3AB² + B³. 200
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