Cramer's Rule gives an explicit formula for the solution of a system of linear equations with as many equations as unknowns, whenever the coefficient matrix has a nonzero determinant, expressing each unknown as the determinant of a matrix formed by replacing one column of the coefficient matrix with the constant terms, divided by the determinant of the coefficient matrix itself. Named for Gabriel Cramer, it is a classical closed-form solution method taught alongside Gaussian elimination.
Facts
StatementFor a system of n linear equations in n unknowns whose coefficient matrix has a nonzero determinant, each unknown equals the determinant of the matrix formed by replacing that unknown's column with the right-hand-side vector, divided by the coefficient matrix's own determinant. 2 Proof YearColin Maclaurin published special cases of the same rule in 1748 and may have known it as early as 1729, per the same cited article. Classification
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1. Wikipedia: Cramer's rule
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
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.
2. Cramer's Rule (Wikipedia)
Wikimedia FoundationLead paragraph, opening sentence
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.
Lead paragraph, attribution sentence
It is named after Gabriel Cramer, who published the rule for an arbitrary number of unknowns in 1750, although Colin Maclaurin also published special cases of the rule in 1748, and possibly knew of it as early as 1729.
In Branch: Linear Algebra, Lead sentence
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as
Proved By: Gabriel Cramer, Lead
It is named after Gabriel Cramer, who published the rule for an arbitrary number of unknowns in 1750, although Colin Maclaurin also published special cases of the rule in 1748, and possibly knew of it as early as 1729.
In Group: Linear Algebra and Matrix Theory, Lead section
In linear algebra, Cramer's rule is an explicit formula for the
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