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- Independent_equation abstract "An independent equation is an equation in a system of simultaneous equations which cannot be derived algebraically from the other equations. The concept typically arises in the context of linear equations. If it is possible to duplicate one of the equations in a system by multiplying each of the other equations by some number (potentially a different number for each equation) and summing the resulting equations, then that equation is dependent on the others. But if this is not possible, then that equation is independent of the others.If an equation is independent of the other equations in its system, then it provides information beyond that which is provided by the other equations. In contrast, if an equation is dependent on the others, then it provides no information not contained in the others collectively, and the equation can be dropped from the system without any information loss.The number of independent equations in a system equals the rank of the augmented matrix of the system—the system's coefficient matrix with one additional column appended, that column being the column vector of constants.The number of independent equations in a system of consistent equations (a system that has at least one solution) can never be greater than the number of unknowns. Equivalently, if a system has more independent equations than unknowns, it is inconsistent and has no solutions.".
- Independent_equation thumbnail Three_Intersecting_Lines.svg?width=300.
- Independent_equation wikiPageID "5957182".
- Independent_equation wikiPageLength "2601".
- Independent_equation wikiPageOutDegree "14".
- Independent_equation wikiPageRevisionID "685096178".
- Independent_equation wikiPageWikiLink Augmented_matrix.
- Independent_equation wikiPageWikiLink Category:Linear_algebra.
- Independent_equation wikiPageWikiLink Coefficient_matrix.
- Independent_equation wikiPageWikiLink Consistent_and_inconsistent_equations.
- Independent_equation wikiPageWikiLink Dependent_and_independent_variables.
- Independent_equation wikiPageWikiLink Equation.
- Independent_equation wikiPageWikiLink Indeterminate_system.
- Independent_equation wikiPageWikiLink Linear_algebra.
- Independent_equation wikiPageWikiLink Linear_equation.
- Independent_equation wikiPageWikiLink Row_and_column_vectors.
- Independent_equation wikiPageWikiLink System_of_linear_equations.
- Independent_equation wikiPageWikiLink File:3_equations_-1.JPG.
- Independent_equation wikiPageWikiLink File:Parallel_Lines.svg.
- Independent_equation wikiPageWikiLink File:Three_Intersecting_Lines.svg.
- Independent_equation wikiPageWikiLinkText "Independent equation".
- Independent_equation wikiPageWikiLinkText "independent equation".
- Independent_equation wikiPageWikiLinkText "independent".
- Independent_equation wikiPageUsesTemplate Template:=.
- Independent_equation wikiPageUsesTemplate Template:Linear-algebra-stub.
- Independent_equation wikiPageUsesTemplate Template:Unreferenced.
- Independent_equation subject Category:Linear_algebra.
- Independent_equation hypernym Equation.
- Independent_equation comment "An independent equation is an equation in a system of simultaneous equations which cannot be derived algebraically from the other equations. The concept typically arises in the context of linear equations. If it is possible to duplicate one of the equations in a system by multiplying each of the other equations by some number (potentially a different number for each equation) and summing the resulting equations, then that equation is dependent on the others.".
- Independent_equation label "Independent equation".
- Independent_equation sameAs Q16979193.
- Independent_equation sameAs m.0fgl86.
- Independent_equation sameAs Q16979193.
- Independent_equation wasDerivedFrom Independent_equation?oldid=685096178.
- Independent_equation depiction Three_Intersecting_Lines.svg.
- Independent_equation isPrimaryTopicOf Independent_equation.