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Cramer's rule (Theorem)

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 $b$




"Cramer's rule" is owned by akrowne.
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example of Cramer's rule (Example) by drini
proof of Cramer's rule (Proof) by rmilson
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Cross-references: column, solution, column vectors, linear equations, matrix
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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 MSC15A15 (Linear and multilinear algebra; matrix theory :: Determinants, permanents, other special matrix functions)

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printing an entry by pahio on 2008-10-22 15:10:05
Hi, is it possible to print the contents of an individual PM entry in page images mode onto paper? How?
I tried it from the File menu of my browser (Opera), and I got the whole contents of the screen.
Jussi
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