Definition:Trivial Solution to Homogeneous Simultaneous Linear Equations
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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
- 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 $1.6$