Math 2.0

Linear and multilinear algebra; matrix theory Definition

Consistent and inconsistent systems

Builds on System of linear equations

Definition

Let FF be a field. A system of linear equations over FF is consistent when it has at least one solution in FnF^n. It is inconsistent when it has no solution.

Remarks

The system x+y=1x + y = 1, x+y=2x + y = 2 over ℝ\R is inconsistent. Every homogeneous system is consistent, because the zero tuple is a solution. The Rouché–Capelli theorem gives a test with ranks: Ax=bAx = b is consistent if and only if rank⁡A=rank⁡[A∣b]\rank A = \rank [A \mid b].

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Further reading

  1. Web https://en.wikipedia.org/wiki/Consistent_and_inconsistent_equations, lead section
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