Question

Which expression gives expansion along \[R_2\]?

Options

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

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

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

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

Answer 1

Expansion along \[R_2\] deletes row 2 and the column containing the selected element. Its signs are \[-,+,-\], so the first and third terms are subtracted.