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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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Summary of Possible Outcomes when Solving a System of Linear Equations: 1. The system may be inconsistent. This happens if a REF obtained from the augmented matrix has a leading 1 in its rightmost column. 2. The system may be consistent. In this case one of the following occurs : (a) Theremaybeauniquesolution.
The parametric form for the general solution to a system of equations is a system of equations for the non-free variables in terms of the free variables. For instance, if x2 and x4 are free, x1 = 2 3x4 x3 = 1 4x4 is a parametric form. Theorem. Every solution to a consistent linear system is obtained by substituting (unique)
Consistency and Dependency. A system of equations is consistent if it has at least one solution. A system is inconsistent if it has no solution.
When r(A) = m is equal to the number of rows of A, then every system of the form A~x = ~b is consistent. Proof of the Corollary: Since [A;~b] has also m rows, r([A;~b]) m. And since every column of A is also a column of [A;~b], we also must have r(A) r([A;~b]). Thus r(A) = m implies that r([A;~b]) = m = r(A).
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.
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How do you know if a system of linear equations is inconsistent?
Is a system of equations consistent or indeterminate?
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Why is a system inconsistent?
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.
