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determinant_of_a_3x3_matrix
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If $\def\mat#1{\begin{bmatrix}#1\end{bmatrix}}A=\mat{a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}}$ is a $3\times 3$ matrix, then \[\det A=a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}.\] Here $C_{ij}$ are the cofactors of $A$.
This formula is called the Laplace expansion of $\det A$ along the first row, since $a_{11}$, $a_{12}$ and $a_{13}$ make up the first row of $A$.
determinant_of_a_3x3_matrix.txt · Last modified: by rupert