The accompanying figure shows known flow rates of hydrocarbons into and out of a network of pipes at an oil refinery. 200 E X3 D Find A so that Ax = X4 150 X6 X5 25 A B x2 175 C (a) Set up a linear system whose solution provides the unknown flow rates. where x = 200 X1 x 2 x3 X4 X5 x6 and y 25 175 200 150 200 Form the system so that the first equation represents node A, the second equation node B, etc. Then take all the variable to one side such that all the constants are on one side and positive. From the equations form the required matrices and enter the appropriate values for A below.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 15EQ
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Question
A =
i
i
i
p.
i
M.
i
M.
i
i
p.
i
Transcribed Image Text:A = i i i p. i M. i M. i i p. i
The accompanying figure shows known flow rates of hydrocarbons into and out of a network of pipes at an oil refinery.
200
X₁
E X3 D
X4'
150
X6
X5
25
A
B
x2
175 C
(a) Set up a linear system whose solution provides the unknown flow rates.
Find A so that Ax = where x =
X1
x 2
x 3
x4
X5
200
X6
and
=
25
175
200
150
200
Form the system so that the first equation represents node A, the second equati node B, etc. Then take all the variable to one side
such that all the constants are on one side and positive. From the equations form the required matrices and enter the appropriate
values for A below.
Transcribed Image Text:The accompanying figure shows known flow rates of hydrocarbons into and out of a network of pipes at an oil refinery. 200 X₁ E X3 D X4' 150 X6 X5 25 A B x2 175 C (a) Set up a linear system whose solution provides the unknown flow rates. Find A so that Ax = where x = X1 x 2 x 3 x4 X5 200 X6 and = 25 175 200 150 200 Form the system so that the first equation represents node A, the second equati node B, etc. Then take all the variable to one side such that all the constants are on one side and positive. From the equations form the required matrices and enter the appropriate values for A below.
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