Definition:Trivial Solution to Homogeneous Simultaneous Linear Equations

Definition

Let $S$ be a system of homogeneous simultaneous linear equations:

$\ds \forall i \in \set {1, 2, \ldots, m}: \sum_{j \mathop = 1}^n \alpha_{i j} x_j = 0$

The solution:

$\tuple {x_1, x_2, \ldots, x_n}$

such that:

$\forall j \in \set {1, 2, \ldots, n}: x_j = 0$

is known as the trivial solution to $S$.

Also see

• Trivial Solution to System of Homogeneous Simultaneous Linear Equations is Solution

• Results about simultaneous linear equations can be found here.

Sources

• 1982: A.O. Morris: Linear Algebra: An Introduction (2nd ed.) ... (previous) ... (next): Chapter $1$: Linear Equations and Matrices: $1.3$ Applications to Linear Equations: Definition $1.6$