Can Non-Homogenous Simultaneous Equations be Solved using Eigenvalues?

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wasi-uz-zaman
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hi
i know how to calculate eigenvalue of given matrix. I want to know if two non homogenous simutaneous equation are given - than can we find its eigenvalue.
 
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I guess what you mean by 'non-homogenous simutaneous equation'

(A-a)x = 0
(B-b)x = 0

In order to understand this set of equations you have to study the commutator [A,B]