I need some help with a linear algebra problem involving traffic flow networks. The goal is to find the flow rates (f1 through f5) and analyze an augmented matrix.When I did this, I got confused in finding the flow rates... my answer doesn't resemble the vector format it should look like (shown in the last figure).Could I get some assistance to better understand how to set up this problem and find the flow rates?Thank you. 300,00080,000+A=Af₂j= hD't£₂ f₂1O-1Wef (4)011100000O1tof₁ - f3 + f5f₂ +F3 -fsfu + f5fyfyf5=0 →4O-110Bс410000faf5 = 160,000-£qfy= 160,000 - fr60,000400-7160,000-1fy fy47-00+ 160,000 -fy = 160,000220,00080,000160,000C300,00060,000160,00080, πουf₁-f3000000I0->(A) 300,000(8)(c) fy + fy = 160,000441100= 220,000f₁ = 220,000+ f3₁ = ₁ + f₂ +60,000f₂ + f₂ = fs +80,080fy = fqfs= fsC220,00080,000160,000Of₁ + f₂ = 300,000→ f₁-f₂fy - 60,000f₂+ fy - fs = 80,000

Answered: Image /qna-images/answer/c23a2a19-3af7-467b-9bfc-c0edfd3ceb15.jpg

Answered: 300,000 80,000 A D В fa C 60,000…

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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I need some help with a linear algebra problem involving traffic flow networks. The goal is to find the flow rates (f₁ through f₅) and analyze an augmented matrix.

When I did this, I got confused in finding the flow rates... my answer doesn't resemble the vector format it should look like (shown in the last figure).

Could I get some assistance to better understand how to set up this problem and find the flow rates?

Thank you.

300,000
80,000+
A=
A
f₂
j= h
D
't
£₂ f₂
1
O
-1
Wef (4)
0
1
11
00000
O
1
to
f₁ - f3 + f5
f₂ +F3 -fs
fu + f5
fy
fy
f5=0 →
4
O
-1
1
0
B
с
410000
fa
f5 = 160,000-£q
fy
= 160,000 - fr
60,000
400-7
160,000
-1
fy fy
47-00
+ 160,000 -fy = 160,000
220,000
80,000
160,000
C
300,000
60,000
160,000
80, που
f₁-f3
00000
0
I
0
->
(A) 300,000
(8)
(c) fy + fy = 160,000
441100
= 220,000
f₁ = 220,000+ f3
₁ = ₁ + f₂ +60,000
f₂ + f₂ = fs +80,080
fy = fq
fs= fs
C
220,000
80,000
160,000
O
f₁ + f₂ = 300,000
→ f₁-f₂fy - 60,000
f₂+ fy - fs = 80,000

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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