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Inconsistent Equation. An equation that has no solution is called an inconsistent equation. The solution set to an inconsistent equation has no members. The set with no mem-bers is called the empty set and it is denoted by the symbol .
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A system which has a solution is called consistent. If a system is inconsistent, a REF obtained from its augmented matrix will include a row of the form 0 0 0 : : : 0 1, i.e. will have a leading 1 in its rightmost column.
In mathematics and particularly in algebra, a system of equations (either linear or nonlinear) is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, when substituted into each of the equations, they make each equation hold true as an identity.
IMPORTANT DEFINITIONS AND THEOREMS REFERENCE SHEET This is a (not quite comprehensive) list of definitions and theorems given in Math 1553. Pay particular attention to the ones inred. For each definition, find an example of something that satisfies the re-quirements of the definition, and an example of something that does not.
A system of linear equations is called inconsistent if it has no solutions. It is called consistent if it has at least one solution. This definition exactly matches the definition for vector equations ( definition in Section 1.2 ).
Definition 2.8 (Consistent, inconsistent and indeterminate systems) A system of equations is said to be consistent if it has a solution, otherwise it is said to be an inconsistent. If a system of equations has more than one solution then it is said to be indeterminate.
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Definition. An inconsistent equation is a linear equation with no solution. It represents lines that are parallel and never intersect.
