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
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