The Lower Colorado River consists of a series of four reservoirs as shown in Fig

Chapter 11, Problem 11.12

(choose chapter or problem)

The Lower Colorado River consists of a series of four reservoirs as shown in Fig. P11.12. Mass balances can be written for each reservoir, and the following set of simultaneous linear algebraic equations results: 13.422 0 0 0 13.422 12.252 0 0 0 12.252 12.377 0 0 0 12.377 11.797 c1 c2 c3 c4 = 750.5 300 102 30 where the right-hand-side vector consists of the loadings of chloride to each of the four lakes and c1, c2, c3, and c4 = the resulting chloride concentrations for Lakes Powell, Mead, Mohave, and Havasu, respectively. (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 column-sum norm, compute the condition number and how many suspect digits would be generated by solving this system.