Problem 13.3 Consider the network of streets with intersections A, B, C and D below. The arrows indicate the direction of traffic flow along the one-way streets, and the numbers refer to the exact number of cars observed to enter or leave A B,C and D during one minute. Each x; denotes the unknown number of cars which passed along the indicated streets during the same period. X1 B X4 X5 4 -A C x2 X3 a) Write down the linear system which describes the the traffic flow, together with all the constraints on the variables xi, i 1,...,5. (Do not perform any operations on your equations: this is done for you in (b).) = b) The reduced row-echelon form of the augmented matrix from part (a) is [1 00-1 0 10] 01 0 1 1 |│ 1 0 0 1 1 1│ 4 0 0 0 0 0 0 | Give the general solution. (Ignore the constraints at this point.) c) If AC were closed due to roadwork, find all possible traffic flows, using your results from (b).
Problem 13.3 Consider the network of streets with intersections A, B, C and D below. The arrows indicate the direction of traffic flow along the one-way streets, and the numbers refer to the exact number of cars observed to enter or leave A B,C and D during one minute. Each x; denotes the unknown number of cars which passed along the indicated streets during the same period. X1 B X4 X5 4 -A C x2 X3 a) Write down the linear system which describes the the traffic flow, together with all the constraints on the variables xi, i 1,...,5. (Do not perform any operations on your equations: this is done for you in (b).) = b) The reduced row-echelon form of the augmented matrix from part (a) is [1 00-1 0 10] 01 0 1 1 |│ 1 0 0 1 1 1│ 4 0 0 0 0 0 0 | Give the general solution. (Ignore the constraints at this point.) c) If AC were closed due to roadwork, find all possible traffic flows, using your results from (b).
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 12CR
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![Problem 13.3 Consider the network of streets with intersections A, B, C and D below. The arrows
indicate the direction of traffic flow along the one-way streets, and the numbers refer to the exact
number of cars observed to enter or leave A B,C and D during one minute. Each x; denotes the
unknown number of cars which passed along the indicated streets during the same period.
X1
B
X4
X5
4
-A
C
x2
X3
a) Write down the linear system which describes the the traffic flow, together with all the
constraints on the variables xi, i 1,...,5. (Do not perform any operations on your equations:
this is done for you in (b).)
=
b) The reduced row-echelon form of the augmented matrix from part (a) is
[1
00-1
0
10]
01 0 1
1 |│
1
0 0 1 1
1│
4
0
0 0 0 0 0 |
Give the general solution. (Ignore the constraints at this point.)
c) If AC were closed due to roadwork, find all possible traffic flows, using your results from (b).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F215cb3f6-bc07-4b31-a07e-679c345e3904%2F0058258d-9adc-4076-b9aa-4b151221c654%2F3gb905d_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 13.3 Consider the network of streets with intersections A, B, C and D below. The arrows
indicate the direction of traffic flow along the one-way streets, and the numbers refer to the exact
number of cars observed to enter or leave A B,C and D during one minute. Each x; denotes the
unknown number of cars which passed along the indicated streets during the same period.
X1
B
X4
X5
4
-A
C
x2
X3
a) Write down the linear system which describes the the traffic flow, together with all the
constraints on the variables xi, i 1,...,5. (Do not perform any operations on your equations:
this is done for you in (b).)
=
b) The reduced row-echelon form of the augmented matrix from part (a) is
[1
00-1
0
10]
01 0 1
1 |│
1
0 0 1 1
1│
4
0
0 0 0 0 0 |
Give the general solution. (Ignore the constraints at this point.)
c) If AC were closed due to roadwork, find all possible traffic flows, using your results from (b).
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