Lower Colorado River (Problem 11.12 in Chapra) My Solutia The Lower Colorado River consists of a series of four reservoirs as shown in Fig. P11.12 in the textbook. Mass balances can be written for each reservoir, and the following set of simultaneous linear algebraic equations results: [ 13.422 0 00; -13.422 12.252 0 0; 0-12.252 12.377 0; 00-12.377 11.797] * [C_1, c_2, c_3, c_4)' = [750.5, 300, 102, 30) where the right-hand-side vector consists of the loadings of chloride to each of the four lakes. The variables c_1, c_2, c_3, and c_4 are the resulting chloride concentrations for Lakes Powell, Mead, Mohave, and Havasu, respectively. Given this information, complete the following tasks: (a) Use the matrix inverse to solve for the concentrations in each of the four lakes. (b) How much must the loading to Lake Powell be reduced for the chloride concentration of Lake Havasu to be 75? (c) Using the matrix 2-norm (spectral norm), compute the condition number and how many suspect digits would be generated by solving this system. Do not round number of significant digits for part (c). You may use the MATLAB condition number function (cond). Hint for part (b): Do not use a negative sign to indicate a reduction, a positive number is expected. Hint for part (c): In MATLAB log is the natural log function, whereas log10 is the base 10 log function.
Lower Colorado River (Problem 11.12 in Chapra) My Solutia The Lower Colorado River consists of a series of four reservoirs as shown in Fig. P11.12 in the textbook. Mass balances can be written for each reservoir, and the following set of simultaneous linear algebraic equations results: [ 13.422 0 00; -13.422 12.252 0 0; 0-12.252 12.377 0; 00-12.377 11.797] * [C_1, c_2, c_3, c_4)' = [750.5, 300, 102, 30) where the right-hand-side vector consists of the loadings of chloride to each of the four lakes. The variables c_1, c_2, c_3, and c_4 are the resulting chloride concentrations for Lakes Powell, Mead, Mohave, and Havasu, respectively. Given this information, complete the following tasks: (a) Use the matrix inverse to solve for the concentrations in each of the four lakes. (b) How much must the loading to Lake Powell be reduced for the chloride concentration of Lake Havasu to be 75? (c) Using the matrix 2-norm (spectral norm), compute the condition number and how many suspect digits would be generated by solving this system. Do not round number of significant digits for part (c). You may use the MATLAB condition number function (cond). Hint for part (b): Do not use a negative sign to indicate a reduction, a positive number is expected. Hint for part (c): In MATLAB log is the natural log function, whereas log10 is the base 10 log function.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
![My Solutions >
Lower Colorado River (Problem 11.12 in Chapra)
The Lower Colorado River consists of a series of four reservoirs as shown in Fig. P11.12 in the textbook. Mass balances can be written for each reservoir, and the
following set of simultaneous linear algebraic equations results:
[ 13.422 0 00;
-13.422 12.252 0 0;
0 -12.252 12.377 0;
00-12.377 11.797]
* [C_1, c_2, c_3, c_4]'
= [750.5, 300, 102, 30]
where the right-hand-side vector consists of the loadings of chloride to each of the four lakes. The variables c_1, c_2, c_3, and c_4 are the resulting chloride
concentrations for Lakes Powell, Mead, Mohave, and Havasu, respectively.
Given this information, complete the following tasks:
(a) Use the matrix inverse to solve for the concentrations in each of the four lakes.
(b) How much must the loading to Lake Powell be reduced for the chloride concentration of Lake Havasu to be 75?
(c) Using the matrix 2-norm (spectral norm), compute the condition number and how many suspect digits would be generated by solving this system.
Do not round number of significant digits for part (c). You may use the MATLAB condition number function (cond).
Hint for part (b): Do not use a negative sign to indicate a reduction, a positive number is expected.
Hint for part (c): In MATLAB log is the natural log function, whereas log10 is the base 10 log function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf13ee5e-a50f-4d35-8bc2-7cd853ccdb4d%2Fb84d9ea1-2720-40b4-bbf7-644a4c16183f%2Ftp53zh5s_processed.png&w=3840&q=75)
Transcribed Image Text:My Solutions >
Lower Colorado River (Problem 11.12 in Chapra)
The Lower Colorado River consists of a series of four reservoirs as shown in Fig. P11.12 in the textbook. Mass balances can be written for each reservoir, and the
following set of simultaneous linear algebraic equations results:
[ 13.422 0 00;
-13.422 12.252 0 0;
0 -12.252 12.377 0;
00-12.377 11.797]
* [C_1, c_2, c_3, c_4]'
= [750.5, 300, 102, 30]
where the right-hand-side vector consists of the loadings of chloride to each of the four lakes. The variables c_1, c_2, c_3, and c_4 are the resulting chloride
concentrations for Lakes Powell, Mead, Mohave, and Havasu, respectively.
Given this information, complete the following tasks:
(a) Use the matrix inverse to solve for the concentrations in each of the four lakes.
(b) How much must the loading to Lake Powell be reduced for the chloride concentration of Lake Havasu to be 75?
(c) Using the matrix 2-norm (spectral norm), compute the condition number and how many suspect digits would be generated by solving this system.
Do not round number of significant digits for part (c). You may use the MATLAB condition number function (cond).
Hint for part (b): Do not use a negative sign to indicate a reduction, a positive number is expected.
Hint for part (c): In MATLAB log is the natural log function, whereas log10 is the base 10 log function.
![1 function [A_inverse,c, del_b1, cond_num, digits]=Chapra_11p12()
2 %% Output
3 % A_inverse: 4x4 Inverse of coefficient matrix
4 %
C:
4x1 solution vector [c1; c2; c3; c4]
5 % del_b1:
6 % cond_num:
7 % digits:
reduction in Lake Powell loading (scalar)
condition number of A, based on spectral norm (scalar)
number of suspect digits in solution, c (scalar)
9 % HINTS: Do not use a negative sign to indicate a reduction for part (b)
10 %
Do not round number of significant digits for part (c)
11 %
Note that, in MATLAB, log is the natural log function,
12 %
whereas log10 is the base 10 log function.
13
14 % Write your code here
15 A=[13.442 0 0 0;
-13.442 12.252 0 0;
O -12.252 12.377 0;
0 0 -12.377 11.797];
16
17
18
19 W=[750.5,3e0,102, 30];
20 C- AI*W
21 end
22 end;
23](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf13ee5e-a50f-4d35-8bc2-7cd853ccdb4d%2Fb84d9ea1-2720-40b4-bbf7-644a4c16183f%2Fjt14u7_processed.png&w=3840&q=75)
Transcribed Image Text:1 function [A_inverse,c, del_b1, cond_num, digits]=Chapra_11p12()
2 %% Output
3 % A_inverse: 4x4 Inverse of coefficient matrix
4 %
C:
4x1 solution vector [c1; c2; c3; c4]
5 % del_b1:
6 % cond_num:
7 % digits:
reduction in Lake Powell loading (scalar)
condition number of A, based on spectral norm (scalar)
number of suspect digits in solution, c (scalar)
9 % HINTS: Do not use a negative sign to indicate a reduction for part (b)
10 %
Do not round number of significant digits for part (c)
11 %
Note that, in MATLAB, log is the natural log function,
12 %
whereas log10 is the base 10 log function.
13
14 % Write your code here
15 A=[13.442 0 0 0;
-13.442 12.252 0 0;
O -12.252 12.377 0;
0 0 -12.377 11.797];
16
17
18
19 W=[750.5,3e0,102, 30];
20 C- AI*W
21 end
22 end;
23
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY