The Lower Colorado River consists of a series of four reservoirs as shown in Figure. Mass balances can be written for each reservoir and the following set of simultaneous linear algebraic equation results:

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 in order 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 thissystem.

Transcribed Image Text:

13.422 750.5 -13.422 12.252 C2 300 102 -12.252 12.377 Сз - 12.377 11.797, 30 C4