Sarrius Rule

Sarryus's rule is a method for calculating the determinant of a third-order matrix . Along with the rule of the triangle, it is intended to introduce clarity into the process of calculating the determinant, thereby reducing the probability of an error. Named after the French mathematician Pierre Frederic Sarrius .

For matrix $3\times 3$ ${\ displaystyle 3 \ times 3}$ $3 \ times3$ :

A={\begin{pmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{pmatrix}}

{\ displaystyle A = {\ begin {pmatrix} a_ {11} & a_ {12} & a_ {13} \\ a_ {21} & a_ {22} & a_ {23} \\ a_ {31} & a_ {32} & a_ {33 } \ end {pmatrix}}}

A = \ begin {pmatrix} a_ {11} & a_ {12} & a_ {13} \\ a_ {21} & a_ {22} & a_ {23} \\ a_ {31} & a_ {32} & a_ {33} \ end {pmatrix}

the determinant is a summation of six works of three elements. The action is performed according to the following scheme:

The first two columns of the matrix are written to the right near the matrix. The products of the elements standing on the lines marked “plus” are added up, then the products of the elements located on the lines marked “minus” are subtracted from the result:

\det(A)=a_{11}a_{22}a_{33}+a_{12}a_{23}a_{31}+a_{13}a_{21}a_{32}-a_{13}a_{22}a_{31}-a_{11}a_{23}a_{32}-a_{12}a_{21}a_{33}

{\ displaystyle \ det (A) = a_ {11} a_ {22} a_ {33} + a_ {12} a_ {23} a_ {31} + a_ {13} a_ {21} a_ {32} -a_ { 13} a_ {22} a_ {31} -a_ {11} a_ {23} a_ {32} -a_ {12} a_ {21} a_ {33}}

\ det (A) = a_ {11} a_ {22} a_ {33} + a_ {12} a_ {23} a_ {31} + a_ {13} a_ {21} a_ {32} -a_ {13} a_ {22} a_ {31} -a_ {11} a_ {23} a_ {32} -a_ {12} a_ {21} a_ {33}

Literature

Gerd Fischer: Analytische Geometrie. 4-te Auflage, Vieweg 1985, ISBN 3-528-37235-4 , P.145 (in German)

Links

Sarrius Rule on Planetmath

Sarrius Rule

Literature

Links

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