[[Linear equations MOC]]
# Homogenous system of linear equations
Similarly to a [[Classifying DEs|Homogeneous linear differential equation]],
the word homogenous here refers to the lack of a constant,
i.e. a homogenous system is one that can be expressed in the form
$$
\begin{align*}
A\vab x = \vab 0
\end{align*}
$$
These have the special property that they are never inconsistent (See [[System of linear equations#Zero solutions]]).
It follows from this immediately that any homogenous system of linear equations
with fewer equations than unknowns
has infinitely many solutions.

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