નિશ્વાયક — ગણિત ધોરણ 12 સાયન્સ — Question

‎ $D=\begin{vmatrix}s+r & p & q \\r & s+p & q \\r & p & s+q\end{vmatrix}$

$\xrightarrow[{{C_{31}}\left( 1 \right)}]{{{C_{21}}\left( 1 \right)}}\begin{vmatrix}s+p+q+r & p & q \\s+p+q+r & s+p & q \\s+p+q+r & p & s+q\end{vmatrix}$

${s = p + q + r}\begin{vmatrix}2s& p & q \\2s & s+p & q \\2s & p & s+q\end{vmatrix}$

$=2s\begin{vmatrix}1 & p & q \\1 & s+p & q \\1 & p & s+q\end{vmatrix}$

$\xrightarrow[{{R_{23}}\left( { - 1} \right)}]{{{R_{21}}\left( { - 1} \right)}}\begin{vmatrix}0 & -s & 0 \\1 & s+p & q \\0 & -s & s\end{vmatrix}2s$

$=s(s).2s\\=2s^3$