how to solve system of linear equations with unorganized unknowns?
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Omidreza Ghafarinejad on 23 Mar 2015
hi everybody. I have a system of n equations n unknowns and there are two forms of this system. in the first form the system of equations is in the form of A*X=Y. in the second form the system of equations is in the form of A*X=B*Y. A and B are the matrix of constant factors. some of the unknowns are in the matrix X and the others are in the matrix Y(X and Y are columns). so the problem is that unknowns are not in one matrix so they are unorganized. i can define unknowns as zero. if there is another way to define unknowns, please let me know. so how can i solve these systems? please guide me how to solve these systems and how to define unknowns? there are several ways to organize unknowns and put them in just one matrix but i want to know if there is any way to solve the system without organizing unknowns. if all the unknowns were in one matrix then it would be easy to solve the system with linsolve in matlab.
John D'Errico on 23 Mar 2015
Edited: John D'Errico on 23 Mar 2015
Just move all of the unknowns to the left hand side.
A*X - B*Y = 0
Think of it like
[A,-B]*[X;Y] = 0
Any knowns in that set among the a and y variables, you move to the right hand side and sum them up. They are all constants. I fail to see the problem. How would you solve it using pencil and paper? (Answer: Exactly the same way.)
My guess is you are getting confused because you think you have TWO sets of unknowns, mixed in with knowns, in both X and Y. In fact, you can do the entire procedure in only several lines of code, fully vectorized. TRY IT! You might surprise yourself. (Take a shot and try it. REALLY. See how it goes. If you still get confused, then just comment here and I'll show you how.)