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Cramer's rule

In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the column…

Applications, Proof & Practical Considerations

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Overview

General case

Proof

Finding inverse matrix

Applications

Algorithm

Geometric interpretation

Inconsistent and indeterminate cases

Practical Considerations

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Map overview Semantic statistics

Cramer's rule

Nodes48
Edges47
Triples53
Avg. degree1.96
Density0.041667
Components1

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Cramer's rule

Top relations

related to Practical Considerations · 10
Cramer's rule → Bareiss, Cramer's, Despite, For, Gaussian, In, Moreover, Strassen's Multiplication Algorithm, Therefore, This
related to A proof by abstract linear algebra · 7
Cramer's rule → Because, Consider, Cramer's, Observe, Since, So, This
related to External links · 6
Cramer's rule → Cramer's, Eric, MathWorld, PlanetMath, Proof, Weisstein
related to Proof · 5
Cramer's rule → Cramer's, Fix, Linearity, The, This
related to A short proof · 4
Cramer's rule → Cramer's, Hence, On, Recall
related to Example 2: An Inconsistent System · 4
Cramer's rule → Applying Cramer's Rule, By, Consider, Therefore
related to Example 1: An Indeterminate System · 3
Cramer's rule → Applying Cramer's Rule, By, Consider
related to Geometric interpretation · 3
Cramer's rule → Cramer's, Given, These
related to Inconsistent and indeterminate cases · 3
Cramer's rule → Cramer's, For, In
related to 2x2 System · 2
Cramer's rule → Applying Cramer's Rule, Consider

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Important terminology

displaystyle rule cramer's matrix system equations column linear determinant determinants solution unknowns consider ldots proof inconsistent nonzero one case indeterminate

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cramer's ruleis aexplicit formula for the solution of a system of linear equations with as many equations as unknowns0.90text
Cramer's rulerelated to 2x2 SystemConsider0.60section
Cramer's rulerelated to 2x2 SystemApplying Cramer's Rule0.60section
Cramer's rulerelated to A proof by abstract linear algebraThis0.60section
Cramer's rulerelated to A proof by abstract linear algebraConsider0.60section
Cramer's rulerelated to A proof by abstract linear algebraCramer's0.60section
Cramer's rulerelated to A proof by abstract linear algebraBecause0.60section
Cramer's rulerelated to A proof by abstract linear algebraObserve0.60section
Cramer's rulerelated to A proof by abstract linear algebraSo0.60section
Cramer's rulerelated to A proof by abstract linear algebraSince0.60section
Cramer's rulerelated to A short proofCramer's0.60section
Cramer's rulerelated to A short proofOn0.60section

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