DLMF:1.3.E2
type: Item
Digital Library of Mathematical Functions ID: 1.3.E2
DLMF defining formula: <math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\det[a_{jk}]=\begin{vmatrix}a_{11}&a_{12}&a_{13}\\ a_{21}&a_{22}&a_{23}\\ a_{31}&a_{32}&a_{33}\end{vmatrix}=a_{11}\begin{vmatrix}a_{22}&a_{23}\\ a_{32}&a_{33}\end{vmatrix}-a_{12}\begin{vmatrix}a_{21}&a_{23}\\ a_{31}&a_{33}\end{vmatrix}+a_{13}\begin{vmatrix}a_{21}&a_{22}\\ a_{31}&a_{32}\end{vmatrix}=a_{11}a_{22}a_{33}-a_{11}a_{23}a_{32}-a_{12}a_{21}a% _{33}+a_{12}a_{23}a_{31}+a_{13}a_{21}a_{32}-a_{13}a_{22}a_{31}.}}" display="inline"> det ⁡ [ a j ⁢ k ] = | a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 | = a 11 ⁢ | a 22 a 23 a 32 a 33 | - a 12 ⁢ | a 21 a 23 a 31 a 33 | + a 13 ⁢ | a 21 a 22 a 31 a 32 | = a 11 ⁢ a 22 ⁢ a 33 - a 11 ⁢ a 23 ⁢ a 32 - a 12 ⁢ a 21 ⁢ a 33 + a 12 ⁢ a 23 ⁢ a 31 + a 13 ⁢ a 21 ⁢ a 32 - a 13 ⁢ a 22 ⁢ a 31 . <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b"> <apply id="p1.1.m1.1.63.2.cmml" xref="p1.1.m1.1.63"> <and id="p1.1.m1.1.63.2a.cmml" xref="p1.1.m1.1.63"/> <apply id="p1.1.m1.1.63.2b.cmml" xref="p1.1.m1.1.63"> <eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/> <apply id="p1.1.m1.1.63.2.2.cmml" xref="p1.1.m1.1.63.2.2"> <determinant id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1"/> <apply id="p1.1.m1.1.63.2.2.1.1.cmml" xref="p1.1.m1.1.63.2.2.1"> <csymbol cd="latexml" id="p1.1.m1.1.63.2.2.1.1.1.cmml" xref="p1.1.m1.1.2">delimited-[]</csymbol> <apply id="p1.1.m1.1.63.2.2.1.2.cmml" xref="p1.1.m1.1.63.2.2.1.2"> <csymbol cd="ambiguous" id="p1.1.m1.1.63.2.2.1.2.1.cmml" xref="p1.1.m1.1.63.2.2.1.2">subscript</csymbol> <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝑎</ci> <apply id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1"> <times id="p1.1.m1.1.4.1.3.cmml" xref="p1.1.m1.1.4.1.3"/> <ci id="p1.1.m1.1.4.1.1.cmml" xref="p1.1.m1.1.4.1.1">𝑗</ci> <ci id="p1.1.m1.1.4.1.2.cmml" xref="p1.1.m1.1.4.1.2">𝑘</ci> </apply> </apply> </apply> </apply> <apply id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.5"> <determinant id="p1.1.m1.1.7.1.1.cmml" xref="p1.1.m1.1.7.2"/>…
comment: Warning: Falling back to standard tex;
Symbols used: Q10739
Symbols used: integer
instance of: Digital Library of Mathematical Functions Formula
MaRDI profile type: MaRDI formula profile