DLMF:1.3.E2 (Q31)

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DLMF:1.3.E2
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    Statements

    DLMF defining formula
    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 . delimited-[] subscript 𝑎 𝑗 𝑘 subscript 𝑎 11 subscript 𝑎 12 subscript 𝑎 13 subscript 𝑎 21 subscript 𝑎 22 subscript 𝑎 23 subscript 𝑎 31 subscript 𝑎 32 subscript 𝑎 33 subscript 𝑎 11 subscript 𝑎 22 subscript 𝑎 23 subscript 𝑎 32 subscript 𝑎 33 subscript 𝑎 12 subscript 𝑎 21 subscript 𝑎 23 subscript 𝑎 31 subscript 𝑎 33 subscript 𝑎 13 subscript 𝑎 21 subscript 𝑎 22 subscript 𝑎 31 subscript 𝑎 32 subscript 𝑎 11 subscript 𝑎 22 subscript 𝑎 33 subscript 𝑎 11 subscript 𝑎 23 subscript 𝑎 32 subscript 𝑎 12 subscript 𝑎 21 subscript 𝑎 33 subscript 𝑎 12 subscript 𝑎 23 subscript 𝑎 31 subscript 𝑎 13 subscript 𝑎 21 subscript 𝑎 32 subscript 𝑎 13 subscript 𝑎 22 subscript 𝑎 31 {\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}.}}
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    Q10739
    DLMF defining formula
    det {\displaystyle{\displaystyle\det}}
    xml-id
    C1.S3.SS1.m1aadec
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    integer
    DLMF defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C1.S1.XMD3.m1adec
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    integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C1.S1.XMD4.m1adec
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    Identifiers

     
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