# How to solve the system of equations?

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Dear,

does anybody has some idea how to solve this system of equations> X*A+B*X'-C=0.

A=[2674.015 1007.506 -979.980 673.29 -1332.007 7.506;-5.317 -1.969 1.750 -1.291 2.777 -1.969;-2808.466 -1058.120 1028.797 -707.075 1399.196 -1058.120;-5363.677 -2020.687 1964.589 -1350.219 2672.592 -2020.687;5382.325 2027.684 -1971.321 1354.875 -2681.975 2027.684;-9.889 -3.691 3.424 -2.442 5.055 -3.692]

B=[-1.679 -1.266 -120.123 -0.166 -0.686 -1.266;-0.525 -0.432 -43.874 -0.0375 -0.303 -0.432;4.714 4.857 685.238 -0.057 5.058 4.857;-0.274 -0.255 -28.164 -0.0077 -0.230 -0.255;1.229 0.805 66.092 0.171 0.208 0.805;-0.525 -0.432 -43.874 -0.037 -0.303 -0.432]

C=[9.931 3.696 -12.773 2.510 -5.066 3.696;3.578 1.306 -10.479 0.916 -1.885 1.306;-65.536 -30.400 -1258.341 -14.196 18.926 -30.400;2.334 0.879 -0.849 0.588 -1.163 0.879;-5.592 -2.142 -7.170 -1.383 2.709 -2.142;3.578 1.306 -10.479 0.916 -1.885 1.306];

Best,

george

x' is transposed X

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Can you make it clear what X, A, B and C are? Are they all square matrices?

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Yes, all 6x6 quadratic matrices. It is like Lyapunov equation but not exactly one of them.

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This looks like a job for matlab.

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This looks like a job for matlab.

Yes, quite.

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Yes, all 6x6 quadratic matrices. It is like Lyapunov equation but not exactly one of them.

The Lyapunov equation is what spring to my mind also. My suggestion is find out as much as you can about that and similar equations.

I am not familiar with the theorems or techniques regarding solutions to matrix equations like that. I have no idea what is in the literature.

The suggestion of using a computer maybe an approach, you might have to resort to numerical methods.

Edited by ajb

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