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So I've been trying to solve a system of 'linear' equations and I understand that for a non trivial solution to exist you have to get the determinant to reduce to zero.

Given that you have an equation which takes the form

(f(x))*A=0, where f(x) is an arbitary function and A is a constant, the solution is either f(x)=0 or A=0.

Now say that for a non trivial solution, I'd require that f(x)=0, is there any methods in general in which I can obtain an expression for A? Let's assume it's a 4 by 4 system of equation.

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# Finding a solution to (A)(B)=0

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