Name the 3 characteristics of a system of linear equations
The three characteristics of a system of linear equations are:
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The three characteristics of a system of linear equations are:
1. Consistency: A system of linear equations is considered consistent if there exists at least one solution that satisfies all the equations in the system. This means that the equations are not contradictory and can be solved simultaneously. In other words, all the equations in the system can be satisfied by a common set of values.
2. Inconsistency: A system of linear equations is considered inconsistent if there is no common solution that satisfies all the equations in the system. Inconsistent systems typically have contradictory equations that cannot be simultaneously satisfied. This means that the system has no solution or is unsolvable.
3. Dependency: A system of linear equations is considered dependent if one or more of the equations in the system can be derived from the other equations. In other words, there is redundancy or duplication among the equations, and one equation can be obtained by adding, subtracting, or multiplying the other equations. Dependent systems have an infinite number of solutions since they are not uniquely determined.
It is important to analyze these three characteristics when solving systems of linear equations as they provide essential information about solution existence, uniqueness, and relationships among the equations.
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