Question 1199356: The Lower Colorado River consists of a series of four reservoirs. Mass balances can be written for each reservoir, and the following set of simultaneous linear algebraic equations results:
* I don't know how to type in matrices here without looking messy, please Google search the above statements to obtain the equation :( *
a) Find normalized eigenvectors for Q, you may use MATLAB or any other software to find your answers. [5 marks]
I already calculated the above part, which the eigenvalues are basically just 11.797, 12.252, 12.377 and 13.422, but I couldn't solve the next question:
b) Hence, using your answer in (a), given  ,  (lambda is the eigenvalue), eigenvalue property of  and  , v3 is the eigenvector obtained from the third eigenvalue, 12.377. Calculate matrix K. [1 mark]
It only worth 1 mark, I think there's a faster way to solve it like by using Cayley-Hamilton Theorem, I'm not really sure, please help me
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website!
I found this link with a solution:
Problem 12.8
The Lower Colorado River consists of a series of four reservoirs as shown in Fig. P12.8. Mass balances can be written for each reservoir and the following set of simultaneous linear algebraic equations results:
https://webstersean.wordpress.com/problems-and-solutions-from-chapters-11-and-12/
I hope it will help.
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