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Mathematics-Online lexicon: Annotation to

Cramer's Rule


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview

For a square LSE $ Ax=b$ the following holds true:

$\displaystyle x_i \operatorname{det} A =
\operatorname{det}
(a_1,\ldots,a_{i-1},b,a_{i+1},\ldots,a_n)\,
,
$

where $ a_j$ denotes the $ j$-th column of the coefficient matrix.

In particular, if $ \operatorname{det}A\ne0$, then we can find the inverse $ B=A^{-1}$ by

$\displaystyle b_{i,j} = \frac{
\operatorname{det}
(a_1,\ldots,a_{i-1},e_j,a_{i+1},\ldots,a_n)}{
\operatorname{det}A}\, .
$


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  automatisch erstellt am 19.  8. 2013