Question

Which expression is the expansion of \[|A|\] along the first column \[C_1\]?

विकल्प

• \[|A|=a_{11}\begin{vmatrix}a_{22}&a_{23}\\a_{32}&a_{33}\end{vmatrix}-a_{12}\begin{vmatrix}a_{21}&a_{23}\\a_{31}&a_{33}\end{vmatrix}+a_{13}\begin{vmatrix}a_{21}&a_{22}\\a_{31}&a_{32}\end{vmatrix}\]

• \[|A|=-a_{11}\begin{vmatrix}a_{22}&a_{23}\\a_{32}&a_{33}\end{vmatrix}+a_{21}\begin{vmatrix}a_{12}&a_{13}\\a_{32}&a_{33}\end{vmatrix}-a_{31}\begin{vmatrix}a_{12}&a_{13}\\a_{22}&a_{23}\end{vmatrix}\]

• \[|A|=a_{11}\begin{vmatrix}a_{22}&a_{23}\\a_{32}&a_{33}\end{vmatrix}-a_{21}\begin{vmatrix}a_{12}&a_{13}\\a_{32}&a_{33}\end{vmatrix}+a_{31}\begin{vmatrix}a_{12}&a_{13}\\a_{22}&a_{23}\end{vmatrix}\]

• \[|A|=a_{11}\begin{vmatrix}a_{12}&a_{13}\\a_{22}&a_{23}\end{vmatrix}-a_{21}\begin{vmatrix}a_{11}&a_{13}\\a_{31}&a_{33}\end{vmatrix}+a_{31}\begin{vmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{vmatrix}\]

Answer 1

For expansion along \[C_1\], use entries \[a_{11},a_{21},a_{31}\] and delete each entry's row and column. The signs down this column are \[+, -, +\].