નિશ્વાયક — ગણિત ધોરણ 12 સાયન્સ — Question

$\begin{vmatrix}0&ab^2&ac^2\\a^2b&0&bc^2\\a^2c&b^2c&0\end{vmatrix}$

$=abc\begin{vmatrix}0&b^2&c^2\\a^2&0&c^2\\a^2&b^2&0\end{vmatrix}$

$R_{21}(-1)=abc\begin{vmatrix}0&b^2&c^2\\a^2&0&c^2\\0&b^2&-c^2\end{vmatrix}$

$R_{31}(-1)=abc\begin{vmatrix}0&b^2&c^2\\a^2&0&c^2\\0&b^2&-c^2\end{vmatrix}$

$=abc \ 2a^2[a^2\cdot b^2-0]$

$=abc \ 2a^2b^2c^2$

$=2a^3b^3c^3$