= Trivial Solution =

A '''homogenous system of equations''' always has a '''trivial solution'''.

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== Description ==

A '''homogenous''' system of equations has a vector of zeros on the RHS, as in:

{{{
┌    ┐ ┌  ┐   ┌  ┐
│ 1 2│ │ x│   │ 0│
│ 3 4│ │ y│ = │ 0│
└    ┘ └  ┘   └  ┘
}}}

Such a system always has a particular solution in the form of ''x=0'' and ''y=0''. This is called the '''trivial solution'''.

If a system has a non-zero constant on the RHS, it is called '''non-homogenous'''.

If a system is known to [[LinearAlgebra/ParticularSolution#Number_of_solutions|have only one unique solution]] ''and'' it is homogenous, it follows that the trivial solution ''is'' the one unique solution.



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CategoryRicottone