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Let $Ax=b$ be the matrix form of a system of $n$ linear equations in $n$ unknowns, with $x$ and $b$ as $n\times 1$ column vectors and $A$ an $n \times n$ matrix. If $\det(A)\ne 0$ then this system has a unique solution, and for each $i$ ($1\le i \le n$ ,
$$ x_i = \frac{\det(M_i)}{\det(A)} $$
where $M_i$ is $A$ with column $i$ replaced by $b$
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"Cramer's rule" is owned by akrowne.
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Cross-references: column, solution, column vectors, linear equations, matrix
There are 5 references to this entry.
This is version 5 of Cramer's rule, born on 2001-10-29, modified 2002-09-21.
Object id is 626, canonical name is CramersRule.
Accessed 24107 times total.
Classification:
| AMS MSC: | 15A15 (Linear and multilinear algebra; matrix theory :: Determinants, permanents, other special matrix functions) |
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Pending Errata and Addenda
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