Definition:Homogeneous Simultaneous Linear Equations

Definition
A system of simultaneous linear equations:


 * $\ds \forall i \in \set {1, 2, \ldots, m}: \sum_{j \mathop = 1}^n \alpha_{i j} x_j = \beta_i$

is referred to as homogeneous :
 * $\forall i \in \set {1, 2, \ldots, m}: \beta_i = 0$

That is: