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**NOn-linear equation, when has a solution??**

For linear system of equations:

[tex] A_{ij}x^{i}=b_{j} [/tex] (implicit sum over repeated indices)

a necessary and sufficient condition to exist is that |detA| >0

but what happens whenever you have a Non-linear equation:

[tex] f(x_{i},x_{j} , x_{k})=b_{j} [/tex] ??

How do you know it will have a solution or not??...

the problem arises mainly in NOn-linear equation theory..how do you know that equation:

[tex] \int_{0}^{\infty} K(x,y,f(x),)dy = g(x) [/tex]

has a solution applying a 'quadrature method' ??